skimage.measure.find_contours(array, level) | Find iso-valued contours in a 2D array for a given level value. |
skimage.measure.regionprops(label_image[, …]) | Measure properties of labeled image regions. |
skimage.measure.perimeter(image[, neighbourhood]) | Calculate total perimeter of all objects in binary image. |
skimage.measure.approximate_polygon(coords, …) | Approximate a polygonal chain with the specified tolerance. |
skimage.measure.subdivide_polygon(coords[, …]) | Subdivision of polygonal curves using B-Splines. |
skimage.measure.ransac(data, model_class, …) | Fit a model to data with the RANSAC (random sample consensus) algorithm. |
skimage.measure.block_reduce(image, block_size) | Down-sample image by applying function to local blocks. |
skimage.measure.moments(image[, order]) | Calculate all raw image moments up to a certain order. |
skimage.measure.moments_central(image[, …]) | Calculate all central image moments up to a certain order. |
skimage.measure.moments_coords(coords[, order]) | Calculate all raw image moments up to a certain order. |
skimage.measure.moments_coords_central(coords) | Calculate all central image moments up to a certain order. |
skimage.measure.moments_normalized(mu[, order]) | Calculate all normalized central image moments up to a certain order. |
skimage.measure.moments_hu(nu) | Calculate Hu’s set of image moments (2D-only). |
skimage.measure.marching_cubes_lewiner(volume) | Lewiner marching cubes algorithm to find surfaces in 3d volumetric data. |
skimage.measure.marching_cubes_classic(volume) | Classic marching cubes algorithm to find surfaces in 3d volumetric data. |
skimage.measure.mesh_surface_area(verts, faces) | Compute surface area, given vertices & triangular faces |
skimage.measure.correct_mesh_orientation(…) | Correct orientations of mesh faces. |
skimage.measure.profile_line(image, src, dst) | Return the intensity profile of an image measured along a scan line. |
skimage.measure.label(input[, neighbors, …]) | Label connected regions of an integer array. |
skimage.measure.points_in_poly(points, verts) | Test whether points lie inside a polygon. |
skimage.measure.grid_points_in_poly(shape, verts) | Test whether points on a specified grid are inside a polygon. |
skimage.measure.compare_ssim(X, Y[, …]) | Compute the mean structural similarity index between two images. |
skimage.measure.compare_mse(im1, im2) | Compute the mean-squared error between two images. |
skimage.measure.compare_nrmse(im_true, im_test) | Compute the normalized root mean-squared error (NRMSE) between two images. |
skimage.measure.compare_psnr(im_true, im_test) | Compute the peak signal to noise ratio (PSNR) for an image. |
skimage.measure.shannon_entropy(image[, base]) | Calculate the Shannon entropy of an image. |
skimage.measure.LineModelND() | Total least squares estimator for N-dimensional lines. |
skimage.measure.CircleModel() | Total least squares estimator for 2D circles. |
skimage.measure.EllipseModel() | Total least squares estimator for 2D ellipses. |
skimage.measure.find_contours(array, level, fully_connected='low', positive_orientation='low') [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: |
|
|---|---|
| Returns: |
|
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 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 (at x=0) and the 1-element (at x=1), and thus would fall at x=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.
| [1] | (1, 2) 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). |
>>> 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. ]])]
skimage.measure.regionprops(label_image, intensity_image=None, cache=True, coordinates=None) [source]
Measure properties of labeled image regions.
| Parameters: |
|
|---|---|
| Returns: |
|
See also
The following properties can be accessed as attributes or keys:
area : int bbox : tuple (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_area : int centroid : array (row, col).convex_area : int convex_image : (H, J) ndarray coords : (N, 2) ndarray (row, col) of the region.eccentricity : float equivalent_diameter : float euler_number : int extent : float area / (rows * cols)
filled_area : int filled_image : (H, J) ndarray image : (H, J) ndarray inertia_tensor : (2, 2) ndarray inertia_tensor_eigvals : tuple intensity_image : ndarray label : int local_centroid : array (row, col), relative to region bounding box.major_axis_length : float max_intensity : float mean_intensity : float min_intensity : float minor_axis_length : float moments : (3, 3) ndarray Spatial moments up to 3rd order:
m_ji = sum{ array(x, y) * x^j * y^i }
where the sum is over the x, y coordinates of the region.
moments_central : (3, 3) ndarray Central moments (translation invariant) up to 3rd order:
mu_ji = sum{ array(x, y) * (x - x_c)^j * (y - y_c)^i }
where the sum is over the x, y coordinates of the region, and x_c and y_c are the coordinates of the region’s centroid.
moments_hu : tuple moments_normalized : (3, 3) ndarray Normalized moments (translation and scale invariant) up to 3rd order:
nu_ji = mu_ji / m_00^[(i+j)/2 + 1]
where m_00 is the zeroth spatial moment.
orientation : float In ‘rc’ coordinates, 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.
In xy coordinates, as above but the angle is now measured from the “x” or horizontal axis.
perimeter : float solidity : float weighted_centroid : array (row, col) weighted with intensity image.weighted_local_centroid : array (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_ji = sum{ array(x, y) * x^j * y^i }
where the sum is over the x, y coordinates of the region.
weighted_moments_central : (3, 3) ndarray Central moments (translation invariant) of intensity image up to 3rd order:
wmu_ji = sum{ array(x, y) * (x - x_c)^j * (y - y_c)^i }
where the sum is over the x, y coordinates of the region, and x_c and y_c are the coordinates of the region’s weighted centroid.
weighted_moments_hu : tuple weighted_moments_normalized : (3, 3) ndarray Normalized moments (translation and scale invariant) of intensity image up to 3rd order:
wnu_ji = wmu_ji / 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])
| [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] | http://en.wikipedia.org/wiki/Image_moment |
>>> 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 (22.729879860483141, 81.912285234465827) >>> # centroid of first labeled object >>> props[0]['centroid'] (22.729879860483141, 81.912285234465827)
skimage.measure.perimeter(image, neighbourhood=4) [source]
Calculate total perimeter of all objects in binary image.
| Parameters: |
|
|---|---|
| Returns: |
|
| [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 |
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: |
|
|---|---|
| Returns: |
|
| [1] | http://en.wikipedia.org/wiki/Ramer-Douglas-Peucker_algorithm |
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: |
|
|---|---|
| Returns: |
|
| [1] | http://mrl.nyu.edu/publications/subdiv-course2000/coursenotes00.pdf |
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) [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:
min_samples random samples from the original data and check whether the set of data is valid (see is_data_valid).model_cls.estimate(*data[random_subset]) and check whether the estimated model is valid (see is_model_valid).model_cls.residuals(*data)) - all data samples with residuals smaller than the residual_threshold are considered as inliers.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: |
|
|---|---|
| Returns: |
|
| [1] | “RANSAC”, Wikipedia, http://en.wikipedia.org/wiki/RANSAC |
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
Robustly estimate geometric transformation:
>>> 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)
>>> model, inliers = ransac((src, dst), SimilarityTransform, 2, 10)
>>> 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], dtype=bool)
skimage.measure.block_reduce(image, block_size, func=<function sum>, cval=0) [source]
Down-sample image by applying function to local blocks.
| Parameters: |
|
|---|---|
| Returns: |
|
>>> 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]]])
skimage.measure.moments(image, order=3) [source]
Calculate all raw image moments up to a certain order.
M[0, 0].M[1, 0] / M[0, 0], M[0, 1] / M[0, 0]}.Note that raw moments are neither translation, scale nor rotation invariant.
| Parameters: |
|
|---|---|
| Returns: |
|
| [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] | http://en.wikipedia.org/wiki/Image_moment |
>>> image = np.zeros((20, 20), dtype=np.double) >>> image[13:17, 13:17] = 1 >>> M = moments(image) >>> cr = M[1, 0] / M[0, 0] >>> cc = M[0, 1] / M[0, 0] >>> cr, cc (14.5, 14.5)
skimage.measure.moments_central(image, center=None, cc=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: |
|
|---|---|
| Returns: |
|
| Other Parameters: | |
| |
| [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] | http://en.wikipedia.org/wiki/Image_moment |
>>> image = np.zeros((20, 20), dtype=np.double)
>>> image[13:17, 13:17] = 1
>>> M = moments(image)
>>> cr = M[1, 0] / M[0, 0]
>>> cc = M[0, 1] / M[0, 0]
>>> moments_central(image, (cr, cc))
array([[ 16., 0., 20., 0.],
[ 0., 0., 0., 0.],
[ 20., 0., 25., 0.],
[ 0., 0., 0., 0.]])
skimage.measure.moments_coords(coords, order=3) [source]
Calculate all raw image moments up to a certain order.
M[0, 0].M[1, 0] / M[0, 0], M[0, 1] / M[0, 0]}.Note that raw moments are neither translation, scale nor rotation invariant.
| Parameters: |
|
|---|---|
| Returns: |
|
| [1] | Johannes Kilian. Simple Image Analysis By Moments. Durham University, version 0.2, Durham, 2001. |
>>> 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_row = M[1, 0] / M[0, 0] >>> centroid_col = M[0, 1] / M[0, 0] >>> centroid_row, centroid_col (14.5, 15.5)
skimage.measure.moments_coords_central(coords, center=None, order=3) [source]
Calculate all central image moments up to a certain order.
M[0, 0].M[1, 0] / M[0, 0], M[0, 1] / M[0, 0]}.Note that raw moments are neither translation, scale nor rotation invariant.
| Parameters: |
|
|---|---|
| Returns: |
|
| [1] | Johannes Kilian. Simple Image Analysis By Moments. Durham University, version 0.2, Durham, 2001. |
>>> 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), 2)
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
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: |
|
|---|---|
| Returns: |
|
| [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] | http://en.wikipedia.org/wiki/Image_moment |
>>> image = np.zeros((20, 20), dtype=np.double)
>>> image[13:17, 13:17] = 1
>>> m = moments(image)
>>> cr = m[0, 1] / m[0, 0]
>>> cc = m[1, 0] / m[0, 0]
>>> mu = moments_central(image, cr, cc)
>>> moments_normalized(mu)
array([[ nan, nan, 0.078125 , 0. ],
[ nan, 0. , 0. , 0. ],
[ 0.078125 , 0. , 0.00610352, 0. ],
[ 0. , 0. , 0. , 0. ]])
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: |
|
|---|---|
| Returns: |
|
| [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] | http://en.wikipedia.org/wiki/Image_moment |
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: |
|
|---|---|
| Returns: |
|
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()
| [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 |
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: |
|
|---|---|
| Returns: |
|
See also
skimage.measure.marching_cubes, skimage.measure.mesh_surface_area
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.
| [1] | (1, 2, 3, 4) 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 |
skimage.measure.mesh_surface_area(verts, faces) [source]
Compute surface area, given vertices & triangular faces
| Parameters: |
|
|---|---|
| Returns: |
|
See also
skimage.measure.marching_cubes, skimage.measure.marching_cubes_classic, skimage.measure.correct_mesh_orientation
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.
skimage.measure.correct_mesh_orientation(volume, verts, faces, spacing=(1.0, 1.0, 1.0), gradient_direction='descent') [source]
Correct orientations of mesh faces.
| Parameters: |
|
|---|---|
| Returns: |
|
Certain applications and mesh processing algorithms require all faces to be oriented in a consistent way. Generally, this means a normal vector points “out” of the meshed shapes. This algorithm corrects the output from skimage.measure.marching_cubes_classic by flipping the orientation of mis-oriented faces.
Because marching cubes could be used to find isosurfaces either on gradient descent (where the desired object has greater values than the exterior) or ascent (where the desired object has lower values than the exterior), the gradient_direction kwarg allows the user to inform this algorithm which is correct. If the resulting mesh appears to be oriented completely incorrectly, try changing this option.
The arguments expected by this function are the exact outputs from skimage.measure.marching_cubes_classic. Only faces is corrected and returned, as the vertices do not change; only the order in which they are referenced.
This algorithm assumes faces provided are all triangles.
skimage.measure.profile_line(image, src, dst, linewidth=1, order=1, mode='constant', cval=0.0) [source]
Return the intensity profile of an image measured along a scan line.
| Parameters: |
|
|---|---|
| Returns: |
|
>>> 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.])
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: |
|
|---|---|
| Returns: |
|
See also
| [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 |
>>> 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]]
skimage.measure.points_in_poly(points, verts) [source]
Test whether points lie inside a polygon.
| Parameters: |
|
|---|---|
| Returns: |
|
See also
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: |
|
|---|---|
| Returns: |
|
See also
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: |
|
|---|---|
| Returns: |
|
| Other Parameters: | |
| |
To match the implementation of Wang et. al. [1], set gaussian_weights to True, sigma to 1.5, and use_sample_covariance to False.
| [1] | (1, 2, 3, 4) 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] | (1, 2) Avanaki, A. N. (2009). Exact global histogram specification optimized for structural similarity. Optical Review, 16, 613-621. http://arxiv.org/abs/0901.0065, DOI:10.1007/s10043-009-0119-z |
skimage.measure.compare_mse(im1, im2) [source]
Compute the mean-squared error between two images.
| Parameters: |
|
|---|---|
| Returns: |
|
skimage.measure.compare_nrmse(im_true, im_test, norm_type='Euclidean') [source]
Compute the normalized root mean-squared error (NRMSE) between two images.
| Parameters: |
|
|---|---|
| Returns: |
|
| [1] | (1, 2) https://en.wikipedia.org/wiki/Root-mean-square_deviation |
skimage.measure.compare_psnr(im_true, im_test, data_range=None) [source]
Compute the peak signal to noise ratio (PSNR) for an image.
| Parameters: |
|
|---|---|
| Returns: |
|
| [1] | https://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio |
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: |
|
|---|---|
| Returns: |
|
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.
| [1] | https://en.wikipedia.org/wiki/Entropy_(information_theory) |
| [2] | https://en.wiktionary.org/wiki/Shannon_entropy |
>>> from skimage import data >>> shannon_entropy(data.camera()) 7.0479552324230861
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
>>> 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: |
|
|---|
__init__() [source]
Initialize self. See help(type(self)) for accurate signature.
estimate(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: |
|
|---|---|
| Returns: |
|
predict(x, axis=0, params=None) [source]
Predict intersection of the estimated line model with a hyperplane orthogonal to a given axis.
| Parameters: |
|
|---|---|
| Returns: |
|
| Raises: |
|
predict_x(y, params=None) [source]
Predict x-coordinates for 2D lines using the estimated model.
Alias for:
predict(y, axis=1)[:, 0]
| Parameters: |
|
|---|---|
| Returns: |
|
predict_y(x, params=None) [source]
Predict y-coordinates for 2D lines using the estimated model.
Alias for:
predict(x, axis=0)[:, 1]
| Parameters: |
|
|---|---|
| Returns: |
|
residuals(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: |
|
|---|---|
| Returns: |
|
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.
>>> 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: |
|
|---|
__init__() [source]
Initialize self. See help(type(self)) for accurate signature.
estimate(data) [source]
Estimate circle model from data using total least squares.
| Parameters: |
|
|---|---|
| Returns: |
|
predict_xy(t, params=None) [source]
Predict x- and y-coordinates using the estimated model.
| Parameters: |
|
|---|---|
| Returns: |
|
residuals(data) [source]
Determine residuals of data to model.
For each point the shortest distance to the circle is returned.
| Parameters: |
|
|---|---|
| Returns: |
|
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
>>> 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: |
|
|---|
__init__() [source]
Initialize self. See help(type(self)) for accurate signature.
estimate(data) [source]
Estimate circle model from data using total least squares.
| Parameters: |
|
|---|---|
| Returns: |
|
| [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(t, params=None) [source]
Predict x- and y-coordinates using the estimated model.
| Parameters: |
|
|---|---|
| Returns: |
|
residuals(data) [source]
Determine residuals of data to model.
For each point the shortest distance to the ellipse is returned.
| Parameters: |
|
|---|---|
| Returns: |
|
© 2011 the scikit-image team
Licensed under the BSD 3-clause License.
http://scikit-image.org/docs/0.14.x/api/skimage.measure.html