Module: measure
¶
|
Approximate a polygonal chain with the specified tolerance. |
|
Down-sample image by applying function to local blocks. |
|
Compute the mean-squared error between two images. |
|
Compute the normalized root mean-squared error (NRMSE) between two images. |
|
Compute the peak signal to noise ratio (PSNR) for an image. |
|
Compute the mean structural similarity index between two images. |
|
Find iso-valued contours in a 2D array for a given level value. |
|
Test whether points on a specified grid are inside a polygon. |
|
Compute the inertia tensor of the input image. |
Compute the eigenvalues of the inertia tensor of the image. |
|
|
Label connected regions of an integer array. |
Classic marching cubes algorithm to find surfaces in 3d volumetric data. |
|
Lewiner marching cubes algorithm to find surfaces in 3d volumetric data. |
|
|
Compute surface area, given vertices & triangular faces |
|
Calculate all raw image moments up to a certain order. |
|
Calculate all central image moments up to a certain order. |
|
Calculate all raw image moments up to a certain order. |
Calculate all central image moments up to a certain order. |
|
Calculate Hu’s set of image moments (2D-only). |
|
|
Calculate all normalized central image moments up to a certain order. |
|
Calculate total perimeter of all objects in binary image. |
|
Test whether points lie inside a polygon. |
|
Return the intensity profile of an image measured along a scan line. |
|
Fit a model to data with the RANSAC (random sample consensus) algorithm. |
|
Measure properties of labeled image regions. |
|
Compute image properties and return them as a pandas-compatible table. |
|
Calculate the Shannon entropy of an image. |
|
Subdivision of polygonal curves using B-Splines. |
Total least squares estimator for 2D circles. |
|
Total least squares estimator for 2D ellipses. |
|
Total least squares estimator for N-dimensional lines. |
approximate_polygon¶
-
skimage.measure.
approximate_polygon
(coords, tolerance)[source]¶ Approximate a polygonal chain with the specified tolerance.
It is based on the Douglas-Peucker algorithm.
Note that the approximated polygon is always within the convex hull of the original polygon.
- Parameters
- coords(N, 2) array
Coordinate array.
- tolerancefloat
Maximum distance from original points of polygon to approximated polygonal chain. If tolerance is 0, the original coordinate array is returned.
- Returns
- coords(M, 2) array
Approximated polygonal chain where M <= N.
References
Examples using skimage.measure.approximate_polygon
¶
block_reduce¶
-
skimage.measure.
block_reduce
(image, block_size, func=<function sum at 0x10991e400>, cval=0)[source]¶ Down-sample image by applying function to local blocks.
- Parameters
- imagendarray
N-dimensional input image.
- block_sizearray_like
Array containing down-sampling integer factor along each axis.
- funccallable
Function object which is used to calculate the return value for each local block. This function must implement an
axis
parameter such asnumpy.sum
ornumpy.min
.- cvalfloat
Constant padding value if image is not perfectly divisible by the block size.
- Returns
- imagendarray
Down-sampled image with same number of dimensions as input image.
Examples
>>> from skimage.measure import block_reduce >>> image = np.arange(3*3*4).reshape(3, 3, 4) >>> image # doctest: +NORMALIZE_WHITESPACE array([[[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]], [[12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23]], [[24, 25, 26, 27], [28, 29, 30, 31], [32, 33, 34, 35]]]) >>> block_reduce(image, block_size=(3, 3, 1), func=np.mean) array([[[16., 17., 18., 19.]]]) >>> image_max1 = block_reduce(image, block_size=(1, 3, 4), func=np.max) >>> image_max1 # doctest: +NORMALIZE_WHITESPACE array([[[11]], [[23]], [[35]]]) >>> image_max2 = block_reduce(image, block_size=(3, 1, 4), func=np.max) >>> image_max2 # doctest: +NORMALIZE_WHITESPACE array([[[27], [31], [35]]])
compare_mse¶
-
skimage.measure.
compare_mse
(im1, im2)[source]¶ Compute the mean-squared error between two images.
- Parameters
- image0, image1ndarray
Images. Any dimensionality, must have same shape.
- Returns
- msefloat
The mean-squared error (MSE) metric.
- Warns
- Deprecated:
New in version 0.16.
This function is deprecated and will be removed in scikit-image 0.18. Please use the function named
mean_squared_error
from themetrics
module instead.
See also
Notes
Changed in version 0.16: This function was renamed from
skimage.measure.compare_mse
toskimage.metrics.mean_squared_error
.
compare_nrmse¶
-
skimage.measure.
compare_nrmse
(im_true, im_test, norm_type='euclidean')[source]¶ Compute the normalized root mean-squared error (NRMSE) between two images.
- Parameters
- image_truendarray
Ground-truth image, same shape as im_test.
- image_testndarray
Test image.
- normalization{‘euclidean’, ‘min-max’, ‘mean’}, optional
Controls the normalization method to use in the denominator of the NRMSE. There is no standard method of normalization across the literature [1]. The methods available here are as follows:
‘euclidean’ : normalize by the averaged Euclidean norm of
im_true
:NRMSE = RMSE * sqrt(N) / || im_true ||
where || . || denotes the Frobenius norm and
N = im_true.size
. This result is equivalent to:NRMSE = || im_true - im_test || / || im_true ||.
‘min-max’ : normalize by the intensity range of
im_true
.‘mean’ : normalize by the mean of
im_true
- Returns
- nrmsefloat
The NRMSE metric.
- Warns
- Deprecated:
New in version 0.16.
This function is deprecated and will be removed in scikit-image 0.18. Please use the function named
normalized_root_mse
from themetrics
module instead.
See also
Notes
Changed in version 0.16: This function was renamed from
skimage.measure.compare_nrmse
toskimage.metrics.normalized_root_mse
.References
compare_psnr¶
-
skimage.measure.
compare_psnr
(im_true, im_test, data_range=None)[source]¶ Compute the peak signal to noise ratio (PSNR) for an image.
- Parameters
- image_truendarray
Ground-truth image, same shape as im_test.
- image_testndarray
Test image.
- data_rangeint, optional
The data range of the input image (distance between minimum and maximum possible values). By default, this is estimated from the image data-type.
- Returns
- psnrfloat
The PSNR metric.
- Warns
- Deprecated:
New in version 0.16.
This function is deprecated and will be removed in scikit-image 0.18. Please use the function named
peak_signal_noise_ratio
from themetrics
module instead.
Notes
Changed in version 0.16: This function was renamed from
skimage.measure.compare_psnr
toskimage.metrics.peak_singal_noise_ratio
.References
compare_ssim¶
-
skimage.measure.
compare_ssim
(X, Y, win_size=None, gradient=False, data_range=None, multichannel=False, gaussian_weights=False, full=False, **kwargs)[source]¶ Compute the mean structural similarity index between two images.
- Parameters
- im1, im2ndarray
Images. Any dimensionality with same shape.
- win_sizeint or None, optional
The side-length of the sliding window used in comparison. Must be an odd value. If gaussian_weights is True, this is ignored and the window size will depend on sigma.
- gradientbool, optional
If True, also return the gradient with respect to im2.
- data_rangefloat, optional
The data range of the input image (distance between minimum and maximum possible values). By default, this is estimated from the image data-type.
- multichannelbool, optional
If True, treat the last dimension of the array as channels. Similarity calculations are done independently for each channel then averaged.
- gaussian_weightsbool, optional
If True, each patch has its mean and variance spatially weighted by a normalized Gaussian kernel of width sigma=1.5.
- fullbool, optional
If True, also return the full structural similarity image.
- Returns
- mssimfloat
The mean structural similarity index over the image.
- gradndarray
The gradient of the structural similarity between im1 and im2 [2]. This is only returned if gradient is set to True.
- Sndarray
The full SSIM image. This is only returned if full is set to True.
- Other Parameters
- use_sample_covariancebool
If True, normalize covariances by N-1 rather than, N where N is the number of pixels within the sliding window.
- K1float
Algorithm parameter, K1 (small constant, see [1]).
- K2float
Algorithm parameter, K2 (small constant, see [1]).
- sigmafloat
Standard deviation for the Gaussian when gaussian_weights is True.
- Warns
- Deprecated:
New in version 0.16.
This function is deprecated and will be removed in scikit-image 0.18. Please use the function named
structural_similarity
from themetrics
module instead.
Notes
To match the implementation of Wang et. al. [1], set gaussian_weights to True, sigma to 1.5, and use_sample_covariance to False.
Changed in version 0.16: This function was renamed from
skimage.measure.compare_ssim
toskimage.metrics.structural_similarity
.References
- 1(1,2,3)
Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P. (2004). Image quality assessment: From error visibility to structural similarity. IEEE Transactions on Image Processing, 13, 600-612. https://ece.uwaterloo.ca/~z70wang/publications/ssim.pdf, DOI:10.1109/TIP.2003.819861
- 2
Avanaki, A. N. (2009). Exact global histogram specification optimized for structural similarity. Optical Review, 16, 613-621. arXiv:0901.0065 DOI:10.1007/s10043-009-0119-z
find_contours¶
-
skimage.measure.
find_contours
(array, level, fully_connected='low', positive_orientation='low', *, mask=None)[source]¶ Find iso-valued contours in a 2D array for a given level value.
Uses the “marching squares” method to compute a the iso-valued contours of the input 2D array for a particular level value. Array values are linearly interpolated to provide better precision for the output contours.
- Parameters
- array2D ndarray of double
Input data in which to find contours.
- levelfloat
Value along which to find contours in the array.
- fully_connectedstr, {‘low’, ‘high’}
Indicates whether array elements below the given level value are to be considered fully-connected (and hence elements above the value will only be face connected), or vice-versa. (See notes below for details.)
- positive_orientationeither ‘low’ or ‘high’
Indicates whether the output contours will produce positively-oriented polygons around islands of low- or high-valued elements. If ‘low’ then contours will wind counter- clockwise around elements below the iso-value. Alternately, this means that low-valued elements are always on the left of the contour. (See below for details.)
- mask2D ndarray of bool, or None
A boolean mask, True where we want to draw contours. Note that NaN values are always excluded from the considered region (
mask
is set toFalse
whereverarray
isNaN
).
- Returns
- contourslist of (n,2)-ndarrays
Each contour is an ndarray of shape
(n, 2)
, consisting of n(row, column)
coordinates along the contour.
Notes
The marching squares algorithm is a special case of the marching cubes algorithm [1]. A simple explanation is available here:
http://www.essi.fr/~lingrand/MarchingCubes/algo.html
There is a single ambiguous case in the marching squares algorithm: when a given
2 x 2
-element square has two high-valued and two low-valued elements, each pair diagonally adjacent. (Where high- and low-valued is with respect to the contour value sought.) In this case, either the high-valued elements can be ‘connected together’ via a thin isthmus that separates the low-valued elements, or vice-versa. When elements are connected together across a diagonal, they are considered ‘fully connected’ (also known as ‘face+vertex-connected’ or ‘8-connected’). Only high-valued or low-valued elements can be fully-connected, the other set will be considered as ‘face-connected’ or ‘4-connected’. By default, low-valued elements are considered fully-connected; this can be altered with the ‘fully_connected’ parameter.Output contours are not guaranteed to be closed: contours which intersect the array edge or a masked-off region (either where mask is False or where array is NaN) will be left open. All other contours will be closed. (The closed-ness of a contours can be tested by checking whether the beginning point is the same as the end point.)
Contours are oriented. By default, array values lower than the contour value are to the left of the contour and values greater than the contour value are to the right. This means that contours will wind counter-clockwise (i.e. in ‘positive orientation’) around islands of low-valued pixels. This behavior can be altered with the ‘positive_orientation’ parameter.
The order of the contours in the output list is determined by the position of the smallest
x,y
(in lexicographical order) coordinate in the contour. This is a side-effect of how the input array is traversed, but can be relied upon.Warning
Array coordinates/values are assumed to refer to the center of the array element. Take a simple example input:
[0, 1]
. The interpolated position of 0.5 in this array is midway between the 0-element (atx=0
) and the 1-element (atx=1
), and thus would fall atx=0.5
.This means that to find reasonable contours, it is best to find contours midway between the expected “light” and “dark” values. In particular, given a binarized array, do not choose to find contours at the low or high value of the array. This will often yield degenerate contours, especially around structures that are a single array element wide. Instead choose a middle value, as above.
References
- 1
Lorensen, William and Harvey E. Cline. Marching Cubes: A High Resolution 3D Surface Construction Algorithm. Computer Graphics (SIGGRAPH 87 Proceedings) 21(4) July 1987, p. 163-170).
Examples
>>> a = np.zeros((3, 3)) >>> a[0, 0] = 1 >>> a array([[1., 0., 0.], [0., 0., 0.], [0., 0., 0.]]) >>> find_contours(a, 0.5) [array([[0. , 0.5], [0.5, 0. ]])]
grid_points_in_poly¶
-
skimage.measure.
grid_points_in_poly
(shape, verts)[source]¶ Test whether points on a specified grid are inside a polygon.
For each
(r, c)
coordinate on a grid, i.e.(0, 0)
,(0, 1)
etc., test whether that point lies inside a polygon.- Parameters
- shapetuple (M, N)
Shape of the grid.
- verts(V, 2) array
Specify the V vertices of the polygon, sorted either clockwise or anti-clockwise. The first point may (but does not need to be) duplicated.
- Returns
- mask(M, N) ndarray of bool
True where the grid falls inside the polygon.
See also
inertia_tensor¶
-
skimage.measure.
inertia_tensor
(image, mu=None)[source]¶ Compute the inertia tensor of the input image.
- Parameters
- imagearray
The input image.
- muarray, optional
The pre-computed central moments of
image
. The inertia tensor computation requires the central moments of the image. If an application requires both the central moments and the inertia tensor (for example,skimage.measure.regionprops
), then it is more efficient to pre-compute them and pass them to the inertia tensor call.
- Returns
- Tarray, shape
(image.ndim, image.ndim)
The inertia tensor of the input image. \(T_{i, j}\) contains the covariance of image intensity along axes \(i\) and \(j\).
- Tarray, shape
References
- 1
https://en.wikipedia.org/wiki/Moment_of_inertia#Inertia_tensor
- 2
Bernd Jähne. Spatio-Temporal Image Processing: Theory and Scientific Applications. (Chapter 8: Tensor Methods) Springer, 1993.
inertia_tensor_eigvals¶
-
skimage.measure.
inertia_tensor_eigvals
(image, mu=None, T=None)[source]¶ Compute the eigenvalues of the inertia tensor of the image.
The inertia tensor measures covariance of the image intensity along the image axes. (See
inertia_tensor
.) The relative magnitude of the eigenvalues of the tensor is thus a measure of the elongation of a (bright) object in the image.- Parameters
- imagearray
The input image.
- muarray, optional
The pre-computed central moments of
image
.- Tarray, shape
(image.ndim, image.ndim)
The pre-computed inertia tensor. If
T
is given,mu
andimage
are ignored.
- Returns
- eigvalslist of float, length
image.ndim
The eigenvalues of the inertia tensor of
image
, in descending order.
- eigvalslist of float, length
Notes
Computing the eigenvalues requires the inertia tensor of the input image. This is much faster if the central moments (
mu
) are provided, or, alternatively, one can provide the inertia tensor (T
) directly.
label¶
-
skimage.measure.
label
(input, neighbors=None, background=None, return_num=False, connectivity=None)[source]¶ Label connected regions of an integer array.
Two pixels are connected when they are neighbors and have the same value. In 2D, they can be neighbors either in a 1- or 2-connected sense. The value refers to the maximum number of orthogonal hops to consider a pixel/voxel a neighbor:
1-connectivity 2-connectivity diagonal connection close-up [ ] [ ] [ ] [ ] [ ] | \ | / | <- hop 2 [ ]--[x]--[ ] [ ]--[x]--[ ] [x]--[ ] | / | \ hop 1 [ ] [ ] [ ] [ ]
- Parameters
- inputndarray of dtype int
Image to label.
- neighbors{4, 8}, int, optional
Whether to use 4- or 8-“connectivity”. In 3D, 4-“connectivity” means connected pixels have to share face, whereas with 8-“connectivity”, they have to share only edge or vertex. Deprecated, use
connectivity
instead.- backgroundint, optional
Consider all pixels with this value as background pixels, and label them as 0. By default, 0-valued pixels are considered as background pixels.
- return_numbool, optional
Whether to return the number of assigned labels.
- connectivityint, optional
Maximum number of orthogonal hops to consider a pixel/voxel as a neighbor. Accepted values are ranging from 1 to input.ndim. If
None
, a full connectivity ofinput.ndim
is used.
- Returns
- labelsndarray of dtype int
Labeled array, where all connected regions are assigned the same integer value.
- numint, optional
Number of labels, which equals the maximum label index and is only returned if return_num is True.
See also
References
- 1
Christophe Fiorio and Jens Gustedt, “Two linear time Union-Find strategies for image processing”, Theoretical Computer Science 154 (1996), pp. 165-181.
- 2
Kensheng Wu, Ekow Otoo and Arie Shoshani, “Optimizing connected component labeling algorithms”, Paper LBNL-56864, 2005, Lawrence Berkeley National Laboratory (University of California), http://repositories.cdlib.org/lbnl/LBNL-56864
Examples
>>> import numpy as np >>> x = np.eye(3).astype(int) >>> print(x) [[1 0 0] [0 1 0] [0 0 1]] >>> print(label(x, connectivity=1)) [[1 0 0] [0 2 0] [0 0 3]] >>> print(label(x, connectivity=2)) [[1 0 0] [0 1 0] [0 0 1]] >>> print(label(x, background=-1)) [[1 2 2] [2 1 2] [2 2 1]] >>> x = np.array([[1, 0, 0], ... [1, 1, 5], ... [0, 0, 0]]) >>> print(label(x)) [[1 0 0] [1 1 2] [0 0 0]]
marching_cubes_classic¶
-
skimage.measure.
marching_cubes_classic
(volume, level=None, spacing=(1.0, 1.0, 1.0), gradient_direction='descent')[source]¶ Classic marching cubes algorithm to find surfaces in 3d volumetric data.
Note that the
marching_cubes()
algorithm is recommended over this algorithm, because it’s faster and produces better results.- Parameters
- volume(M, N, P) array of doubles
Input data volume to find isosurfaces. Will be cast to np.float64.
- levelfloat
Contour value to search for isosurfaces in volume. If not given or None, the average of the min and max of vol is used.
- spacinglength-3 tuple of floats
Voxel spacing in spatial dimensions corresponding to numpy array indexing dimensions (M, N, P) as in volume.
- gradient_directionstring
Controls if the mesh was generated from an isosurface with gradient descent toward objects of interest (the default), or the opposite. The two options are: * descent : Object was greater than exterior * ascent : Exterior was greater than object
- Returns
- verts(V, 3) array
Spatial coordinates for V unique mesh vertices. Coordinate order matches input volume (M, N, P).
- faces(F, 3) array
Define triangular faces via referencing vertex indices from
verts
. This algorithm specifically outputs triangles, so each face has exactly three indices.
See also
skimage.measure.marching_cubes
skimage.measure.mesh_surface_area
Notes
The marching cubes algorithm is implemented as described in [1]. A simple explanation is available here:
http://www.essi.fr/~lingrand/MarchingCubes/algo.html
There are several known ambiguous cases in the marching cubes algorithm. Using point labeling as in [1], Figure 4, as shown:
v8 ------ v7 / | / | y / | / | ^ z v4 ------ v3 | | / | v5 ----|- v6 |/ (note: NOT right handed!) | / | / ----> x | / | / v1 ------ v2
Most notably, if v4, v8, v2, and v6 are all >= level (or any generalization of this case) two parallel planes are generated by this algorithm, separating v4 and v8 from v2 and v6. An equally valid interpretation would be a single connected thin surface enclosing all four points. This is the best known ambiguity, though there are others.
This algorithm does not attempt to resolve such ambiguities; it is a naive implementation of marching cubes as in [1], but may be a good beginning for work with more recent techniques (Dual Marching Cubes, Extended Marching Cubes, Cubic Marching Squares, etc.).
Because of interactions between neighboring cubes, the isosurface(s) generated by this algorithm are NOT guaranteed to be closed, particularly for complicated contours. Furthermore, this algorithm does not guarantee a single contour will be returned. Indeed, ALL isosurfaces which cross level will be found, regardless of connectivity.
The output is a triangular mesh consisting of a set of unique vertices and connecting triangles. The order of these vertices and triangles in the output list is determined by the position of the smallest
x,y,z
(in lexicographical order) coordinate in the contour. This is a side-effect of how the input array is traversed, but can be relied upon.The generated mesh guarantees coherent orientation as of version 0.12.
To quantify the area of an isosurface generated by this algorithm, pass outputs directly into
skimage.measure.mesh_surface_area
.References
- 1(1,2,3)
Lorensen, William and Harvey E. Cline. Marching Cubes: A High Resolution 3D Surface Construction Algorithm. Computer Graphics (SIGGRAPH 87 Proceedings) 21(4) July 1987, p. 163-170). DOI:10.1145/37401.37422
marching_cubes_lewiner¶
-
skimage.measure.
marching_cubes_lewiner
(volume, level=None, spacing=(1.0, 1.0, 1.0), gradient_direction='descent', step_size=1, allow_degenerate=True, use_classic=False)[source]¶ Lewiner marching cubes algorithm to find surfaces in 3d volumetric data.
In contrast to
marching_cubes_classic()
, this algorithm is faster, resolves ambiguities, and guarantees topologically correct results. Therefore, this algorithm generally a better choice, unless there is a specific need for the classic algorithm.- Parameters
- volume(M, N, P) array
Input data volume to find isosurfaces. Will internally be converted to float32 if necessary.
- levelfloat
Contour value to search for isosurfaces in volume. If not given or None, the average of the min and max of vol is used.
- spacinglength-3 tuple of floats
Voxel spacing in spatial dimensions corresponding to numpy array indexing dimensions (M, N, P) as in volume.
- gradient_directionstring
Controls if the mesh was generated from an isosurface with gradient descent toward objects of interest (the default), or the opposite, considering the left-hand rule. The two options are: * descent : Object was greater than exterior * ascent : Exterior was greater than object
- step_sizeint
Step size in voxels. Default 1. Larger steps yield faster but coarser results. The result will always be topologically correct though.
- allow_degeneratebool
Whether to allow degenerate (i.e. zero-area) triangles in the end-result. Default True. If False, degenerate triangles are removed, at the cost of making the algorithm slower.
- use_classicbool
If given and True, the classic marching cubes by Lorensen (1987) is used. This option is included for reference purposes. Note that this algorithm has ambiguities and is not guaranteed to produce a topologically correct result. The results with using this option are not generally the same as the
marching_cubes_classic()
function.
- Returns
- verts(V, 3) array
Spatial coordinates for V unique mesh vertices. Coordinate order matches input volume (M, N, P).
- faces(F, 3) array
Define triangular faces via referencing vertex indices from
verts
. This algorithm specifically outputs triangles, so each face has exactly three indices.- normals(V, 3) array
The normal direction at each vertex, as calculated from the data.
- values(V, ) array
Gives a measure for the maximum value of the data in the local region near each vertex. This can be used by visualization tools to apply a colormap to the mesh.
Notes
The algorithm [1] is an improved version of Chernyaev’s Marching Cubes 33 algorithm. It is an efficient algorithm that relies on heavy use of lookup tables to handle the many different cases, keeping the algorithm relatively easy. This implementation is written in Cython, ported from Lewiner’s C++ implementation.
To quantify the area of an isosurface generated by this algorithm, pass verts and faces to
skimage.measure.mesh_surface_area
.Regarding visualization of algorithm output, to contour a volume named myvolume about the level 0.0, using the
mayavi
package:>>> from mayavi import mlab >>> verts, faces, normals, values = marching_cubes_lewiner(myvolume, 0.0) >>> mlab.triangular_mesh([vert[0] for vert in verts], ... [vert[1] for vert in verts], ... [vert[2] for vert in verts], ... faces) >>> mlab.show()
Similarly using the
visvis
package:>>> import visvis as vv >>> verts, faces, normals, values = marching_cubes_lewiner(myvolume, 0.0) >>> vv.mesh(np.fliplr(verts), faces, normals, values) >>> vv.use().Run()
References
- 1
Thomas Lewiner, Helio Lopes, Antonio Wilson Vieira and Geovan Tavares. Efficient implementation of Marching Cubes’ cases with topological guarantees. Journal of Graphics Tools 8(2) pp. 1-15 (december 2003). DOI:10.1080/10867651.2003.10487582
Examples using skimage.measure.marching_cubes_lewiner
¶
mesh_surface_area¶
-
skimage.measure.
mesh_surface_area
(verts, faces)[source]¶ Compute surface area, given vertices & triangular faces
- Parameters
- verts(V, 3) array of floats
Array containing (x, y, z) coordinates for V unique mesh vertices.
- faces(F, 3) array of ints
List of length-3 lists of integers, referencing vertex coordinates as provided in verts
- Returns
- areafloat
Surface area of mesh. Units now [coordinate units] ** 2.
See also
skimage.measure.marching_cubes
skimage.measure.marching_cubes_classic
Notes
The arguments expected by this function are the first two outputs from skimage.measure.marching_cubes. For unit correct output, ensure correct spacing was passed to skimage.measure.marching_cubes.
This algorithm works properly only if the
faces
provided are all triangles.
moments¶
-
skimage.measure.
moments
(image, order=3)[source]¶ Calculate all raw image moments up to a certain order.
- The following properties can be calculated from raw image moments:
Area as:
M[0, 0]
.Centroid as: {
M[1, 0] / M[0, 0]
,M[0, 1] / M[0, 0]
}.
Note that raw moments are neither translation, scale nor rotation invariant.
- Parameters
- imagenD double or uint8 array
Rasterized shape as image.
- orderint, optional
Maximum order of moments. Default is 3.
- Returns
- m(
order + 1
,order + 1
) array Raw image moments.
- m(
References
- 1
Wilhelm Burger, Mark Burge. Principles of Digital Image Processing: Core Algorithms. Springer-Verlag, London, 2009.
- 2
B. Jähne. Digital Image Processing. Springer-Verlag, Berlin-Heidelberg, 6. edition, 2005.
- 3
T. H. Reiss. Recognizing Planar Objects Using Invariant Image Features, from Lecture notes in computer science, p. 676. Springer, Berlin, 1993.
- 4
Examples
>>> image = np.zeros((20, 20), dtype=np.double) >>> image[13:17, 13:17] = 1 >>> M = moments(image) >>> centroid = (M[1, 0] / M[0, 0], M[0, 1] / M[0, 0]) >>> centroid (14.5, 14.5)
moments_central¶
-
skimage.measure.
moments_central
(image, center=None, order=3, **kwargs)[source]¶ Calculate all central image moments up to a certain order.
The center coordinates (cr, cc) can be calculated from the raw moments as: {
M[1, 0] / M[0, 0]
,M[0, 1] / M[0, 0]
}.Note that central moments are translation invariant but not scale and rotation invariant.
- Parameters
- imagenD double or uint8 array
Rasterized shape as image.
- centertuple of float, optional
Coordinates of the image centroid. This will be computed if it is not provided.
- orderint, optional
The maximum order of moments computed.
- Returns
- mu(
order + 1
,order + 1
) array Central image moments.
- mu(
References
- 1
Wilhelm Burger, Mark Burge. Principles of Digital Image Processing: Core Algorithms. Springer-Verlag, London, 2009.
- 2
B. Jähne. Digital Image Processing. Springer-Verlag, Berlin-Heidelberg, 6. edition, 2005.
- 3
T. H. Reiss. Recognizing Planar Objects Using Invariant Image Features, from Lecture notes in computer science, p. 676. Springer, Berlin, 1993.
- 4
Examples
>>> image = np.zeros((20, 20), dtype=np.double) >>> image[13:17, 13:17] = 1 >>> M = moments(image) >>> centroid = (M[1, 0] / M[0, 0], M[0, 1] / M[0, 0]) >>> moments_central(image, centroid) array([[16., 0., 20., 0.], [ 0., 0., 0., 0.], [20., 0., 25., 0.], [ 0., 0., 0., 0.]])
moments_coords¶
-
skimage.measure.
moments_coords
(coords, order=3)[source]¶ Calculate all raw image moments up to a certain order.
- The following properties can be calculated from raw image moments:
Area as:
M[0, 0]
.Centroid as: {
M[1, 0] / M[0, 0]
,M[0, 1] / M[0, 0]
}.
Note that raw moments are neither translation, scale nor rotation invariant.
- Parameters
- coords(N, D) double or uint8 array
Array of N points that describe an image of D dimensionality in Cartesian space.
- orderint, optional
Maximum order of moments. Default is 3.
- Returns
- M(
order + 1
,order + 1
, …) array Raw image moments. (D dimensions)
- M(
References
- 1
Johannes Kilian. Simple Image Analysis By Moments. Durham University, version 0.2, Durham, 2001.
Examples
>>> coords = np.array([[row, col] ... for row in range(13, 17) ... for col in range(14, 18)], dtype=np.double) >>> M = moments_coords(coords) >>> centroid = (M[1, 0] / M[0, 0], M[0, 1] / M[0, 0]) >>> centroid (14.5, 15.5)
moments_coords_central¶
-
skimage.measure.
moments_coords_central
(coords, center=None, order=3)[source]¶ Calculate all central image moments up to a certain order.
- The following properties can be calculated from raw image moments:
Area as:
M[0, 0]
.Centroid as: {
M[1, 0] / M[0, 0]
,M[0, 1] / M[0, 0]
}.
Note that raw moments are neither translation, scale nor rotation invariant.
- Parameters
- coords(N, D) double or uint8 array
Array of N points that describe an image of D dimensionality in Cartesian space. A tuple of coordinates as returned by
np.nonzero
is also accepted as input.- centertuple of float, optional
Coordinates of the image centroid. This will be computed if it is not provided.
- orderint, optional
Maximum order of moments. Default is 3.
- Returns
- Mc(
order + 1
,order + 1
, …) array Central image moments. (D dimensions)
- Mc(
References
- 1
Johannes Kilian. Simple Image Analysis By Moments. Durham University, version 0.2, Durham, 2001.
Examples
>>> coords = np.array([[row, col] ... for row in range(13, 17) ... for col in range(14, 18)]) >>> moments_coords_central(coords) array([[16., 0., 20., 0.], [ 0., 0., 0., 0.], [20., 0., 25., 0.], [ 0., 0., 0., 0.]])
As seen above, for symmetric objects, odd-order moments (columns 1 and 3, rows 1 and 3) are zero when centered on the centroid, or center of mass, of the object (the default). If we break the symmetry by adding a new point, this no longer holds:
>>> coords2 = np.concatenate((coords, [[17, 17]]), axis=0) >>> np.round(moments_coords_central(coords2), ... decimals=2) # doctest: +NORMALIZE_WHITESPACE array([[17. , 0. , 22.12, -2.49], [ 0. , 3.53, 1.73, 7.4 ], [25.88, 6.02, 36.63, 8.83], [ 4.15, 19.17, 14.8 , 39.6 ]])
Image moments and central image moments are equivalent (by definition) when the center is (0, 0):
>>> np.allclose(moments_coords(coords), ... moments_coords_central(coords, (0, 0))) True
moments_hu¶
-
skimage.measure.
moments_hu
(nu)[source]¶ Calculate Hu’s set of image moments (2D-only).
Note that this set of moments is proofed to be translation, scale and rotation invariant.
- Parameters
- nu(M, M) array
Normalized central image moments, where M must be > 4.
- Returns
- nu(7,) array
Hu’s set of image moments.
References
- 1
M. K. Hu, “Visual Pattern Recognition by Moment Invariants”, IRE Trans. Info. Theory, vol. IT-8, pp. 179-187, 1962
- 2
Wilhelm Burger, Mark Burge. Principles of Digital Image Processing: Core Algorithms. Springer-Verlag, London, 2009.
- 3
B. Jähne. Digital Image Processing. Springer-Verlag, Berlin-Heidelberg, 6. edition, 2005.
- 4
T. H. Reiss. Recognizing Planar Objects Using Invariant Image Features, from Lecture notes in computer science, p. 676. Springer, Berlin, 1993.
- 5
moments_normalized¶
-
skimage.measure.
moments_normalized
(mu, order=3)[source]¶ Calculate all normalized central image moments up to a certain order.
Note that normalized central moments are translation and scale invariant but not rotation invariant.
- Parameters
- mu(M,[ …,] M) array
Central image moments, where M must be greater than or equal to
order
.- orderint, optional
Maximum order of moments. Default is 3.
- Returns
- nu(
order + 1
,[ …,]order + 1
) array Normalized central image moments.
- nu(
References
- 1
Wilhelm Burger, Mark Burge. Principles of Digital Image Processing: Core Algorithms. Springer-Verlag, London, 2009.
- 2
B. Jähne. Digital Image Processing. Springer-Verlag, Berlin-Heidelberg, 6. edition, 2005.
- 3
T. H. Reiss. Recognizing Planar Objects Using Invariant Image Features, from Lecture notes in computer science, p. 676. Springer, Berlin, 1993.
- 4
Examples
>>> image = np.zeros((20, 20), dtype=np.double) >>> image[13:17, 13:17] = 1 >>> m = moments(image) >>> centroid = (m[0, 1] / m[0, 0], m[1, 0] / m[0, 0]) >>> mu = moments_central(image, centroid) >>> moments_normalized(mu) array([[ nan, nan, 0.078125 , 0. ], [ nan, 0. , 0. , 0. ], [0.078125 , 0. , 0.00610352, 0. ], [0. , 0. , 0. , 0. ]])
perimeter¶
-
skimage.measure.
perimeter
(image, neighbourhood=4)[source]¶ Calculate total perimeter of all objects in binary image.
- Parameters
- image(N, M) ndarray
2D binary image.
- neighbourhood4 or 8, optional
Neighborhood connectivity for border pixel determination. It is used to compute the contour. A higher neighbourhood widens the border on which the perimeter is computed.
- Returns
- perimeterfloat
Total perimeter of all objects in binary image.
References
- 1
K. Benkrid, D. Crookes. Design and FPGA Implementation of a Perimeter Estimator. The Queen’s University of Belfast. http://www.cs.qub.ac.uk/~d.crookes/webpubs/papers/perimeter.doc
Examples
>>> from skimage import data, util >>> from skimage.measure import label >>> # coins image (binary) >>> img_coins = data.coins() > 110 >>> # total perimeter of all objects in the image >>> perimeter(img_coins, neighbourhood=4) # doctest: +ELLIPSIS 7796.867... >>> perimeter(img_coins, neighbourhood=8) # doctest: +ELLIPSIS 8806.268...
points_in_poly¶
-
skimage.measure.
points_in_poly
(points, verts)[source]¶ Test whether points lie inside a polygon.
- Parameters
- points(N, 2) array
Input points,
(x, y)
.- verts(M, 2) array
Vertices of the polygon, sorted either clockwise or anti-clockwise. The first point may (but does not need to be) duplicated.
- Returns
- mask(N,) array of bool
True if corresponding point is inside the polygon.
See also
profile_line¶
-
skimage.measure.
profile_line
(image, src, dst, linewidth=1, order=1, mode='constant', cval=0.0, *, reduce_func=<function mean at 0x109923950>)[source]¶ Return the intensity profile of an image measured along a scan line.
- Parameters
- imagenumeric array, shape (M, N[, C])
The image, either grayscale (2D array) or multichannel (3D array, where the final axis contains the channel information).
- src2-tuple of numeric scalar (float or int)
The start point of the scan line.
- dst2-tuple of numeric scalar (float or int)
The end point of the scan line. The destination point is included in the profile, in contrast to standard numpy indexing.
- linewidthint, optional
Width of the scan, perpendicular to the line
- orderint in {0, 1, 2, 3, 4, 5}, optional
The order of the spline interpolation to compute image values at non-integer coordinates. 0 means nearest-neighbor interpolation.
- mode{‘constant’, ‘nearest’, ‘reflect’, ‘mirror’, ‘wrap’}, optional
How to compute any values falling outside of the image.
- cvalfloat, optional
If mode is ‘constant’, what constant value to use outside the image.
- reduce_funccallable, optional
Function used to calculate the aggregation of pixel values perpendicular to the profile_line direction when linewidth > 1. If set to None the unreduced array will be returned.
- Returns
- return_valuearray
The intensity profile along the scan line. The length of the profile is the ceil of the computed length of the scan line.
Examples
>>> x = np.array([[1, 1, 1, 2, 2, 2]]) >>> img = np.vstack([np.zeros_like(x), x, x, x, np.zeros_like(x)]) >>> img array([[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [1, 1, 1, 2, 2, 2], [1, 1, 1, 2, 2, 2], [0, 0, 0, 0, 0, 0]]) >>> profile_line(img, (2, 1), (2, 4)) array([1., 1., 2., 2.]) >>> profile_line(img, (1, 0), (1, 6), cval=4) array([1., 1., 1., 2., 2., 2., 4.])
The destination point is included in the profile, in contrast to standard numpy indexing. For example:
>>> profile_line(img, (1, 0), (1, 6)) # The final point is out of bounds array([1., 1., 1., 2., 2., 2., 0.]) >>> profile_line(img, (1, 0), (1, 5)) # This accesses the full first row array([1., 1., 1., 2., 2., 2.])
For different reduce_func inputs:
>>> profile_line(img, (1, 0), (1, 3), linewidth=3, reduce_func=np.mean) array([0.66666667, 0.66666667, 0.66666667, 1.33333333]) >>> profile_line(img, (1, 0), (1, 3), linewidth=3, reduce_func=np.max) array([1, 1, 1, 2]) >>> profile_line(img, (1, 0), (1, 3), linewidth=3, reduce_func=np.sum) array([2, 2, 2, 4])
The unreduced array will be returned when reduce_func is None or when reduce_func acts on each pixel value individually.
>>> profile_line(img, (1, 2), (4, 2), linewidth=3, order=0, ... reduce_func=None) array([[1, 1, 2], [1, 1, 2], [1, 1, 2], [0, 0, 0]]) >>> profile_line(img, (1, 0), (1, 3), linewidth=3, reduce_func=np.sqrt) array([[1. , 1. , 0. ], [1. , 1. , 0. ], [1. , 1. , 0. ], [1.41421356, 1.41421356, 0. ]])
ransac¶
-
skimage.measure.
ransac
(data, model_class, min_samples, residual_threshold, is_data_valid=None, is_model_valid=None, max_trials=100, stop_sample_num=inf, stop_residuals_sum=0, stop_probability=1, random_state=None, initial_inliers=None)[source]¶ Fit a model to data with the RANSAC (random sample consensus) algorithm.
RANSAC is an iterative algorithm for the robust estimation of parameters from a subset of inliers from the complete data set. Each iteration performs the following tasks:
Select min_samples random samples from the original data and check whether the set of data is valid (see is_data_valid).
Estimate a model to the random subset (model_cls.estimate(*data[random_subset]) and check whether the estimated model is valid (see is_model_valid).
Classify all data as inliers or outliers by calculating the residuals to the estimated model (model_cls.residuals(*data)) - all data samples with residuals smaller than the residual_threshold are considered as inliers.
Save estimated model as best model if number of inlier samples is maximal. In case the current estimated model has the same number of inliers, it is only considered as the best model if it has less sum of residuals.
These steps are performed either a maximum number of times or until one of the special stop criteria are met. The final model is estimated using all inlier samples of the previously determined best model.
- Parameters
- data[list, tuple of] (N, …) array
Data set to which the model is fitted, where N is the number of data points and the remaining dimension are depending on model requirements. If the model class requires multiple input data arrays (e.g. source and destination coordinates of
skimage.transform.AffineTransform
), they can be optionally passed as tuple or list. Note, that in this case the functionsestimate(*data)
,residuals(*data)
,is_model_valid(model, *random_data)
andis_data_valid(*random_data)
must all take each data array as separate arguments.- model_classobject
Object with the following object methods:
success = estimate(*data)
residuals(*data)
where success indicates whether the model estimation succeeded (True or None for success, False for failure).
- min_samplesint in range (0, N)
The minimum number of data points to fit a model to.
- residual_thresholdfloat larger than 0
Maximum distance for a data point to be classified as an inlier.
- is_data_validfunction, optional
This function is called with the randomly selected data before the model is fitted to it: is_data_valid(*random_data).
- is_model_validfunction, optional
This function is called with the estimated model and the randomly selected data: is_model_valid(model, *random_data), .
- max_trialsint, optional
Maximum number of iterations for random sample selection.
- stop_sample_numint, optional
Stop iteration if at least this number of inliers are found.
- stop_residuals_sumfloat, optional
Stop iteration if sum of residuals is less than or equal to this threshold.
- stop_probabilityfloat in range [0, 1], optional
RANSAC iteration stops if at least one outlier-free set of the training data is sampled with
probability >= stop_probability
, depending on the current best model’s inlier ratio and the number of trials. This requires to generate at least N samples (trials):N >= log(1 - probability) / log(1 - e**m)
where the probability (confidence) is typically set to a high value such as 0.99, and e is the current fraction of inliers w.r.t. the total number of samples.
- random_stateint, RandomState instance or None, optional
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
- initial_inliersarray-like of bool, shape (N,), optional
Initial samples selection for model estimation
- Returns
- modelobject
Best model with largest consensus set.
- inliers(N, ) array
Boolean mask of inliers classified as
True
.
References
- 1
“RANSAC”, Wikipedia, https://en.wikipedia.org/wiki/RANSAC
Examples
Generate ellipse data without tilt and add noise:
>>> t = np.linspace(0, 2 * np.pi, 50) >>> xc, yc = 20, 30 >>> a, b = 5, 10 >>> x = xc + a * np.cos(t) >>> y = yc + b * np.sin(t) >>> data = np.column_stack([x, y]) >>> np.random.seed(seed=1234) >>> data += np.random.normal(size=data.shape)
Add some faulty data:
>>> data[0] = (100, 100) >>> data[1] = (110, 120) >>> data[2] = (120, 130) >>> data[3] = (140, 130)
Estimate ellipse model using all available data:
>>> model = EllipseModel() >>> model.estimate(data) True >>> np.round(model.params) # doctest: +SKIP array([ 72., 75., 77., 14., 1.])
Estimate ellipse model using RANSAC:
>>> ransac_model, inliers = ransac(data, EllipseModel, 20, 3, max_trials=50) >>> abs(np.round(ransac_model.params)) array([20., 30., 5., 10., 0.]) >>> inliers # doctest: +SKIP array([False, False, False, False, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True], dtype=bool) >>> sum(inliers) > 40 True
RANSAC can be used to robustly estimate a geometric transformation. In this section, we also show how to use a proportion of the total samples, rather than an absolute number.
>>> from skimage.transform import SimilarityTransform >>> np.random.seed(0) >>> src = 100 * np.random.rand(50, 2) >>> model0 = SimilarityTransform(scale=0.5, rotation=1, translation=(10, 20)) >>> dst = model0(src) >>> dst[0] = (10000, 10000) >>> dst[1] = (-100, 100) >>> dst[2] = (50, 50) >>> ratio = 0.5 # use half of the samples >>> min_samples = int(ratio * len(src)) >>> model, inliers = ransac((src, dst), SimilarityTransform, min_samples, 10, ... initial_inliers=np.ones(len(src), dtype=bool)) >>> inliers array([False, False, False, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True])
regionprops¶
-
skimage.measure.
regionprops
(label_image, intensity_image=None, cache=True, coordinates=None)[source]¶ Measure properties of labeled image regions.
- Parameters
- label_image(N, M) ndarray
Labeled input image. Labels with value 0 are ignored.
Changed in version 0.14.1: Previously,
label_image
was processed bynumpy.squeeze
and so any number of singleton dimensions was allowed. This resulted in inconsistent handling of images with singleton dimensions. To recover the old behaviour, useregionprops(np.squeeze(label_image), ...)
.- intensity_image(N, M) ndarray, optional
Intensity (i.e., input) image with same size as labeled image. Default is None.
- cachebool, optional
Determine whether to cache calculated properties. The computation is much faster for cached properties, whereas the memory consumption increases.
- coordinatesDEPRECATED
This argument is deprecated and will be removed in a future version of scikit-image.
See Coordinate conventions for more details.
Deprecated since version 0.16.0: Use “rc” coordinates everywhere. It may be sufficient to call
numpy.transpose
on your label image to get the same values as 0.15 and earlier. However, for some properties, the transformation will be less trivial. For example, the new orientation is \(\frac{\pi}{2}\) plus the old orientation.
- Returns
- propertieslist of RegionProperties
Each item describes one labeled region, and can be accessed using the attributes listed below.
See also
Notes
The following properties can be accessed as attributes or keys:
- areaint
Number of pixels of the region.
- bboxtuple
Bounding box
(min_row, min_col, max_row, max_col)
. Pixels belonging to the bounding box are in the half-open interval[min_row; max_row)
and[min_col; max_col)
.- bbox_areaint
Number of pixels of bounding box.
- centroidarray
Centroid coordinate tuple
(row, col)
.- convex_areaint
Number of pixels of convex hull image, which is the smallest convex polygon that encloses the region.
- convex_image(H, J) ndarray
Binary convex hull image which has the same size as bounding box.
- coords(N, 2) ndarray
Coordinate list
(row, col)
of the region.- eccentricityfloat
Eccentricity of the ellipse that has the same second-moments as the region. The eccentricity is the ratio of the focal distance (distance between focal points) over the major axis length. The value is in the interval [0, 1). When it is 0, the ellipse becomes a circle.
- equivalent_diameterfloat
The diameter of a circle with the same area as the region.
- euler_numberint
Euler characteristic of region. Computed as number of objects (= 1) subtracted by number of holes (8-connectivity).
- extentfloat
Ratio of pixels in the region to pixels in the total bounding box. Computed as
area / (rows * cols)
- filled_areaint
Number of pixels of the region will all the holes filled in. Describes the area of the filled_image.
- filled_image(H, J) ndarray
Binary region image with filled holes which has the same size as bounding box.
- image(H, J) ndarray
Sliced binary region image which has the same size as bounding box.
- inertia_tensorndarray
Inertia tensor of the region for the rotation around its mass.
- inertia_tensor_eigvalstuple
The eigenvalues of the inertia tensor in decreasing order.
- intensity_imagendarray
Image inside region bounding box.
- labelint
The label in the labeled input image.
- local_centroidarray
Centroid coordinate tuple
(row, col)
, relative to region bounding box.- major_axis_lengthfloat
The length of the major axis of the ellipse that has the same normalized second central moments as the region.
- max_intensityfloat
Value with the greatest intensity in the region.
- mean_intensityfloat
Value with the mean intensity in the region.
- min_intensityfloat
Value with the least intensity in the region.
- minor_axis_lengthfloat
The length of the minor axis of the ellipse that has the same normalized second central moments as the region.
- moments(3, 3) ndarray
Spatial moments up to 3rd order:
m_ij = sum{ array(row, col) * row^i * col^j }
where the sum is over the row, col coordinates of the region.
- moments_central(3, 3) ndarray
Central moments (translation invariant) up to 3rd order:
mu_ij = sum{ array(row, col) * (row - row_c)^i * (col - col_c)^j }
where the sum is over the row, col coordinates of the region, and row_c and col_c are the coordinates of the region’s centroid.
- moments_hutuple
Hu moments (translation, scale and rotation invariant).
- moments_normalized(3, 3) ndarray
Normalized moments (translation and scale invariant) up to 3rd order:
nu_ij = mu_ij / m_00^[(i+j)/2 + 1]
where m_00 is the zeroth spatial moment.
- orientationfloat
Angle between the 0th axis (rows) and the major axis of the ellipse that has the same second moments as the region, ranging from -pi/2 to pi/2 counter-clockwise.
- perimeterfloat
Perimeter of object which approximates the contour as a line through the centers of border pixels using a 4-connectivity.
- slicetuple of slices
A slice to extract the object from the source image.
- solidityfloat
Ratio of pixels in the region to pixels of the convex hull image.
- weighted_centroidarray
Centroid coordinate tuple
(row, col)
weighted with intensity image.- weighted_local_centroidarray
Centroid coordinate tuple
(row, col)
, relative to region bounding box, weighted with intensity image.- weighted_moments(3, 3) ndarray
Spatial moments of intensity image up to 3rd order:
wm_ij = sum{ array(row, col) * row^i * col^j }
where the sum is over the row, col coordinates of the region.
- weighted_moments_central(3, 3) ndarray
Central moments (translation invariant) of intensity image up to 3rd order:
wmu_ij = sum{ array(row, col) * (row - row_c)^i * (col - col_c)^j }
where the sum is over the row, col coordinates of the region, and row_c and col_c are the coordinates of the region’s weighted centroid.
- weighted_moments_hutuple
Hu moments (translation, scale and rotation invariant) of intensity image.
- weighted_moments_normalized(3, 3) ndarray
Normalized moments (translation and scale invariant) of intensity image up to 3rd order:
wnu_ij = wmu_ij / wm_00^[(i+j)/2 + 1]
where
wm_00
is the zeroth spatial moment (intensity-weighted area).
Each region also supports iteration, so that you can do:
for prop in region: print(prop, region[prop])
References
- 1
Wilhelm Burger, Mark Burge. Principles of Digital Image Processing: Core Algorithms. Springer-Verlag, London, 2009.
- 2
B. Jähne. Digital Image Processing. Springer-Verlag, Berlin-Heidelberg, 6. edition, 2005.
- 3
T. H. Reiss. Recognizing Planar Objects Using Invariant Image Features, from Lecture notes in computer science, p. 676. Springer, Berlin, 1993.
- 4
Examples
>>> from skimage import data, util >>> from skimage.measure import label >>> img = util.img_as_ubyte(data.coins()) > 110 >>> label_img = label(img, connectivity=img.ndim) >>> props = regionprops(label_img) >>> # centroid of first labeled object >>> props[0].centroid (22.72987986048314, 81.91228523446583) >>> # centroid of first labeled object >>> props[0]['centroid'] (22.72987986048314, 81.91228523446583)
regionprops_table¶
-
skimage.measure.
regionprops_table
(label_image, intensity_image=None, properties=('label', 'bbox'), *, cache=True, separator='-')[source]¶ Compute image properties and return them as a pandas-compatible table.
The table is a dictionary mapping column names to value arrays. See Notes section below for details.
- Parameters
- label_image(N, M) ndarray
Labeled input image. Labels with value 0 are ignored.
- intensity_image(N, M) ndarray, optional
Intensity (i.e., input) image with same size as labeled image. Default is None.
- propertiestuple or list of str, optional
Properties that will be included in the resulting dictionary For a list of available properties, please see
regionprops()
. Users should remember to add “label” to keep track of region identities.- cachebool, optional
Determine whether to cache calculated properties. The computation is much faster for cached properties, whereas the memory consumption increases.
- separatorstr, optional
For non-scalar properties not listed in OBJECT_COLUMNS, each element will appear in its own column, with the index of that element separated from the property name by this separator. For example, the inertia tensor of a 2D region will appear in four columns:
inertia_tensor-0-0
,inertia_tensor-0-1
,inertia_tensor-1-0
, andinertia_tensor-1-1
(where the separator is-
).Object columns are those that cannot be split in this way because the number of columns would change depending on the object. For example,
image
andcoords
.
- Returns
- out_dictdict
Dictionary mapping property names to an array of values of that property, one value per region. This dictionary can be used as input to pandas
DataFrame
to map property names to columns in the frame and regions to rows.
Notes
Each column contains either a scalar property, an object property, or an element in a multidimensional array.
Properties with scalar values for each region, such as “eccentricity”, will appear as a float or int array with that property name as key.
Multidimensional properties of fixed size for a given image dimension, such as “centroid” (every centroid will have three elements in a 3D image, no matter the region size), will be split into that many columns, with the name {property_name}{separator}{element_num} (for 1D properties), {property_name}{separator}{elem_num0}{separator}{elem_num1} (for 2D properties), and so on.
For multidimensional properties that don’t have a fixed size, such as “image” (the image of a region varies in size depending on the region size), an object array will be used, with the corresponding property name as the key.
Examples
>>> from skimage import data, util, measure >>> image = data.coins() >>> label_image = measure.label(image > 110, connectivity=image.ndim) >>> props = regionprops_table(label_image, image, ... properties=['label', 'inertia_tensor', ... 'inertia_tensor_eigvals']) >>> props # doctest: +ELLIPSIS +SKIP {'label': array([ 1, 2, ...]), ... 'inertia_tensor-0-0': array([ 4.012...e+03, 8.51..., ...]), ... ..., 'inertia_tensor_eigvals-1': array([ 2.67...e+02, 2.83..., ...])}
The resulting dictionary can be directly passed to pandas, if installed, to obtain a clean DataFrame:
>>> import pandas as pd # doctest: +SKIP >>> data = pd.DataFrame(props) # doctest: +SKIP >>> data.head() # doctest: +SKIP label inertia_tensor-0-0 ... inertia_tensor_eigvals-1 0 1 4012.909888 ... 267.065503 1 2 8.514739 ... 2.834806 2 3 0.666667 ... 0.000000 3 4 0.000000 ... 0.000000 4 5 0.222222 ... 0.111111
[5 rows x 7 columns]
shannon_entropy¶
-
skimage.measure.
shannon_entropy
(image, base=2)[source]¶ Calculate the Shannon entropy of an image.
The Shannon entropy is defined as S = -sum(pk * log(pk)), where pk are frequency/probability of pixels of value k.
- Parameters
- image(N, M) ndarray
Grayscale input image.
- basefloat, optional
The logarithmic base to use.
- Returns
- entropyfloat
Notes
The returned value is measured in bits or shannon (Sh) for base=2, natural unit (nat) for base=np.e and hartley (Hart) for base=10.
References
- 1
- 2
Examples
>>> from skimage import data >>> shannon_entropy(data.camera()) 7.047955232423086
subdivide_polygon¶
-
skimage.measure.
subdivide_polygon
(coords, degree=2, preserve_ends=False)[source]¶ Subdivision of polygonal curves using B-Splines.
Note that the resulting curve is always within the convex hull of the original polygon. Circular polygons stay closed after subdivision.
- Parameters
- coords(N, 2) array
Coordinate array.
- degree{1, 2, 3, 4, 5, 6, 7}, optional
Degree of B-Spline. Default is 2.
- preserve_endsbool, optional
Preserve first and last coordinate of non-circular polygon. Default is False.
- Returns
- coords(M, 2) array
Subdivided coordinate array.
References
Examples using skimage.measure.subdivide_polygon
¶
CircleModel
¶
-
class
skimage.measure.
CircleModel
[source]¶ Bases:
skimage.measure.fit.BaseModel
Total least squares estimator for 2D circles.
The functional model of the circle is:
r**2 = (x - xc)**2 + (y - yc)**2
This estimator minimizes the squared distances from all points to the circle:
min{ sum((r - sqrt((x_i - xc)**2 + (y_i - yc)**2))**2) }
A minimum number of 3 points is required to solve for the parameters.
Examples
>>> t = np.linspace(0, 2 * np.pi, 25) >>> xy = CircleModel().predict_xy(t, params=(2, 3, 4)) >>> model = CircleModel() >>> model.estimate(xy) True >>> tuple(np.round(model.params, 5)) (2.0, 3.0, 4.0) >>> res = model.residuals(xy) >>> np.abs(np.round(res, 9)) array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
- Attributes
- paramstuple
Circle model parameters in the following order xc, yc, r.
-
estimate
(self, data)[source]¶ Estimate circle model from data using total least squares.
- Parameters
- data(N, 2) array
N points with
(x, y)
coordinates, respectively.
- Returns
- successbool
True, if model estimation succeeds.
-
predict_xy
(self, t, params=None)[source]¶ Predict x- and y-coordinates using the estimated model.
- Parameters
- tarray
Angles in circle in radians. Angles start to count from positive x-axis to positive y-axis in a right-handed system.
- params(3, ) array, optional
Optional custom parameter set.
- Returns
- xy(…, 2) array
Predicted x- and y-coordinates.
EllipseModel
¶
-
class
skimage.measure.
EllipseModel
[source]¶ Bases:
skimage.measure.fit.BaseModel
Total least squares estimator for 2D ellipses.
The functional model of the ellipse is:
xt = xc + a*cos(theta)*cos(t) - b*sin(theta)*sin(t) yt = yc + a*sin(theta)*cos(t) + b*cos(theta)*sin(t) d = sqrt((x - xt)**2 + (y - yt)**2)
where
(xt, yt)
is the closest point on the ellipse to(x, y)
. Thus d is the shortest distance from the point to the ellipse.The estimator is based on a least squares minimization. The optimal solution is computed directly, no iterations are required. This leads to a simple, stable and robust fitting method.
The
params
attribute contains the parameters in the following order:xc, yc, a, b, theta
Examples
>>> xy = EllipseModel().predict_xy(np.linspace(0, 2 * np.pi, 25), ... params=(10, 15, 4, 8, np.deg2rad(30))) >>> ellipse = EllipseModel() >>> ellipse.estimate(xy) True >>> np.round(ellipse.params, 2) array([10. , 15. , 4. , 8. , 0.52]) >>> np.round(abs(ellipse.residuals(xy)), 5) array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
- Attributes
- paramstuple
Ellipse model parameters in the following order xc, yc, a, b, theta.
-
estimate
(self, data)[source]¶ Estimate circle model from data using total least squares.
- Parameters
- data(N, 2) array
N points with
(x, y)
coordinates, respectively.
- Returns
- successbool
True, if model estimation succeeds.
References
- 1
Halir, R.; Flusser, J. “Numerically stable direct least squares fitting of ellipses”. In Proc. 6th International Conference in Central Europe on Computer Graphics and Visualization. WSCG (Vol. 98, pp. 125-132).
-
predict_xy
(self, t, params=None)[source]¶ Predict x- and y-coordinates using the estimated model.
- Parameters
- tarray
Angles in circle in radians. Angles start to count from positive x-axis to positive y-axis in a right-handed system.
- params(5, ) array, optional
Optional custom parameter set.
- Returns
- xy(…, 2) array
Predicted x- and y-coordinates.
LineModelND
¶
-
class
skimage.measure.
LineModelND
[source]¶ Bases:
skimage.measure.fit.BaseModel
Total least squares estimator for N-dimensional lines.
In contrast to ordinary least squares line estimation, this estimator minimizes the orthogonal distances of points to the estimated line.
Lines are defined by a point (origin) and a unit vector (direction) according to the following vector equation:
X = origin + lambda * direction
Examples
>>> x = np.linspace(1, 2, 25) >>> y = 1.5 * x + 3 >>> lm = LineModelND() >>> lm.estimate(np.array([x, y]).T) True >>> tuple(np.round(lm.params, 5)) (array([1.5 , 5.25]), array([0.5547 , 0.83205])) >>> res = lm.residuals(np.array([x, y]).T) >>> np.abs(np.round(res, 9)) array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]) >>> np.round(lm.predict_y(x[:5]), 3) array([4.5 , 4.562, 4.625, 4.688, 4.75 ]) >>> np.round(lm.predict_x(y[:5]), 3) array([1. , 1.042, 1.083, 1.125, 1.167])
- Attributes
- paramstuple
Line model parameters in the following order origin, direction.
-
estimate
(self, data)[source]¶ Estimate line model from data.
This minimizes the sum of shortest (orthogonal) distances from the given data points to the estimated line.
- Parameters
- data(N, dim) array
N points in a space of dimensionality dim >= 2.
- Returns
- successbool
True, if model estimation succeeds.
-
predict
(self, x, axis=0, params=None)[source]¶ Predict intersection of the estimated line model with a hyperplane orthogonal to a given axis.
- Parameters
- x(n, 1) array
Coordinates along an axis.
- axisint
Axis orthogonal to the hyperplane intersecting the line.
- params(2, ) array, optional
Optional custom parameter set in the form (origin, direction).
- Returns
- data(n, m) array
Predicted coordinates.
- Raises
- ValueError
If the line is parallel to the given axis.
-
predict_x
(self, y, params=None)[source]¶ Predict x-coordinates for 2D lines using the estimated model.
Alias for:
predict(y, axis=1)[:, 0]
- Parameters
- yarray
y-coordinates.
- params(2, ) array, optional
Optional custom parameter set in the form (origin, direction).
- Returns
- xarray
Predicted x-coordinates.
-
predict_y
(self, x, params=None)[source]¶ Predict y-coordinates for 2D lines using the estimated model.
Alias for:
predict(x, axis=0)[:, 1]
- Parameters
- xarray
x-coordinates.
- params(2, ) array, optional
Optional custom parameter set in the form (origin, direction).
- Returns
- yarray
Predicted y-coordinates.
-
residuals
(self, data, params=None)[source]¶ Determine residuals of data to model.
For each point, the shortest (orthogonal) distance to the line is returned. It is obtained by projecting the data onto the line.
- Parameters
- data(N, dim) array
N points in a space of dimension dim.
- params(2, ) array, optional
Optional custom parameter set in the form (origin, direction).
- Returns
- residuals(N, ) array
Residual for each data point.


---
layout: default
title: Bug Bounty - Wikimedia Security Team
---
Unfortunately, as the Wikimedia Foundation is a non-profit and charitable organization, it does not pay out bug bounties for disclosing security issues in our projects.
This list is not exhaustive, but should be used as a guide for both in-scope and out-of-scope vulnerabilities, and under which domains they are applicable.
For more information on how to report a security issue in MediaWiki or Wikimedia sites, please see the Reporting Security Bugs page on MediaWiki.org or at HackerOne.
In-scope domains
- mediawiki.org
- w.wiki
- wikibooks.org
- wikidata.org
- wikimedia.com
- wikimedia.org
- wikimediafoundation.org
- wikinews.org
- wikipedia.org
- wikinews.org
- wikisource.org
- wikiversity.org
- wikivoyage.org
- wiktionary.org
Examples of in-scope vulnerabilities
- Remote Code Execution (RCE)
- SQL injection (SQLi)
- Authorization bypass/escalation
- Sensitive information leaks
- Cross-site scripting (XSS)
- Cross-site request forgery (CSRF)
Examples of out-of-scope vulnerabilities
- SPF configuration, or lack thereof
- DKIM configuration, or lack thereof
- DMARC configuration, or lack thereof
- Clickjacking, also known as a "UI redress attack"
- That "anyone can edit" our projects
- Source code disclosures (unless it's a password/auth key); our code is open source
- Assumed vulnerabilities based upon version numbers only


ngShow
ng
The ngShow
directive shows or hides the given HTML element based on the expression
provided to the ngShow attribute. The element is shown or hidden by removing or adding
the ng-hide
CSS class onto the element. The .ng-hide
CSS class is predefined
in AngularJS and sets the display style to none (using an !important flag).
For CSP mode please add angular-csp.css
to your html file (see ngCsp
).

When the ngShow expression evaluates to false then the ng-hide CSS class is added to the class attribute on the element causing it to become hidden. When true, the ng-hide CSS class is removed from the element causing the element not to appear hidden.
You may be wondering why !important is used for the .ng-hide CSS class. This is because the .ng-hide
selector
can be easily overridden by heavier selectors. For example, something as simple
as changing the display style on a HTML list item would make hidden elements appear visible.
This also becomes a bigger issue when dealing with CSS frameworks.
By using !important, the show and hide behavior will work as expected despite any clash between CSS selector specificity (when !important isn't used with any conflicting styles). If a developer chooses to override the styling to change how to hide an element then it is just a matter of using !important in their own CSS code.
If you wish to change the hide behavior with ngShow/ngHide then this can be achieved by restating the styles for the .ng-hide class in CSS:
.ng-hide {display:block!important;//this is just another form of hiding an element position:absolute; top:-9999px; left:-9999px; }
Just remember to include the important flag so the CSS override will function.
Animations in ngShow/ngHide work with the show and hide events that are triggered when the directive expression is true and false. This system works like the animation system present with ngClass except that you must also include the !important flag to override the display property so that you can perform an animation when the element is hidden during the time of the animation.
// //a working example can be found at the bottom of this page // .my-element.ng-hide-add, .my-element.ng-hide-remove { transition:0.5s linear all; display:block!important; } .my-element.ng-hide-add { ... } .my-element.ng-hide-add.ng-hide-add-active { ... } .my-element.ng-hide-remove { ... } .my-element.ng-hide-remove.ng-hide-remove-active { ... }
<ANY ng-show="{expression}"> ... </ANY>
| Param | Type | Details |
|---|---|---|
| ngShow | expression | If the expression is truthy then the element is shown or hidden respectively. |


Bob Pay Test
All cards test
Visa credit card test
Visa debit card test
Credit card test
Visa card test
Bob Pay And Visa card test