Module: metrics
¶
Compute Adapted Rand error as defined by the SNEMI3D contest. |
|
|
Return the contingency table for all regions in matched segmentations. |
|
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. |
|
Return symmetric conditional entropies associated with the VI. |
adapted_rand_error¶
-
skimage.metrics.
adapted_rand_error
(image_true=None, image_test=None, *, table=None, ignore_labels=(0, ))[source]¶ Compute Adapted Rand error as defined by the SNEMI3D contest. [R406]
- Parameters
image_true : ndarray of int
Ground-truth label image, same shape as im_test.
image_test : ndarray of int
Test image.
table : scipy.sparse array in crs format, optional
A contingency table built with skimage.evaluate.contingency_table. If None, it will be computed on the fly.
ignore_labels : sequence of int, optional
Labels to ignore. Any part of the true image labeled with any of these values will not be counted in the score.
- Returns
are : float
The adapted Rand error; equal to \(1 - \frac{2pr}{p + r}\), where
p
andr
are the precision and recall described below.prec : float
The adapted Rand precision: this is the number of pairs of pixels that have the same label in the test label image and in the true image, divided by the number in the test image.
rec : float
The adapted Rand recall: this is the number of pairs of pixels that have the same label in the test label image and in the true image, divided by the number in the true image.
Notes
Pixels with label 0 in the true segmentation are ignored in the score.
References
- R406(1,2)
Arganda-Carreras I, Turaga SC, Berger DR, et al. (2015) Crowdsourcing the creation of image segmentation algorithms for connectomics. Front. Neuroanat. 9:142. DOI:10.3389/fnana.2015.00142
Examples using skimage.metrics.adapted_rand_error
¶
contingency_table¶
-
skimage.metrics.
contingency_table
(im_true, im_test, *, ignore_labels=(), normalize=False)[source]¶ Return the contingency table for all regions in matched segmentations.
- Parameters
im_true : ndarray of int
Ground-truth label image, same shape as im_test.
im_test : ndarray of int
Test image.
ignore_labels : sequence of int, optional
Labels to ignore. Any part of the true image labeled with any of these values will not be counted in the score.
normalize : bool
Determines if the contingency table is normalized by pixel count.
- Returns
cont : scipy.sparse.csr_matrix
A contingency table. cont[i, j] will equal the number of voxels labeled i in im_true and j in im_test.
mean_squared_error¶
-
skimage.metrics.
mean_squared_error
(image0, image1)[source]¶ Compute the mean-squared error between two images.
- Parameters
image0, image1 : ndarray
Images. Any dimensionality, must have same shape.
- Returns
mse : float
The mean-squared error (MSE) metric.
Notes
Changed in version 0.16: This function was renamed from
skimage.measure.compare_mse
toskimage.metrics.mean_squared_error
.
Examples using skimage.metrics.mean_squared_error
¶
normalized_root_mse¶
-
skimage.metrics.
normalized_root_mse
(image_true, image_test, *, normalization='euclidean')[source]¶ Compute the normalized root mean-squared error (NRMSE) between two images.
- Parameters
image_true : ndarray
Ground-truth image, same shape as im_test.
image_test : ndarray
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 [R407]. 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
nrmse : float
The NRMSE metric.
Notes
Changed in version 0.16: This function was renamed from
skimage.measure.compare_nrmse
toskimage.metrics.normalized_root_mse
.References
peak_signal_noise_ratio¶
-
skimage.metrics.
peak_signal_noise_ratio
(image_true, image_test, *, data_range=None)[source]¶ Compute the peak signal to noise ratio (PSNR) for an image.
- Parameters
image_true : ndarray
Ground-truth image, same shape as im_test.
image_test : ndarray
Test image.
data_range : int, 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
psnr : float
The PSNR metric.
Notes
Changed in version 0.16: This function was renamed from
skimage.measure.compare_psnr
toskimage.metrics.peak_signal_noise_ratio
.References
Examples using skimage.metrics.peak_signal_noise_ratio
¶
structural_similarity¶
-
skimage.metrics.
structural_similarity
(im1, im2, *, 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, im2 : ndarray
Images. Any dimensionality with same shape.
win_size : int 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.
gradient : bool, optional
If True, also return the gradient with respect to im2.
data_range : float, 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.
multichannel : bool, optional
If True, treat the last dimension of the array as channels. Similarity calculations are done independently for each channel then averaged.
gaussian_weights : bool, optional
If True, each patch has its mean and variance spatially weighted by a normalized Gaussian kernel of width sigma=1.5.
full : bool, optional
If True, also return the full structural similarity image.
- Returns
mssim : float
The mean structural similarity index over the image.
grad : ndarray
The gradient of the structural similarity between im1 and im2 [R410]. This is only returned if gradient is set to True.
S : ndarray
The full SSIM image. This is only returned if full is set to True.
- Other Parameters
use_sample_covariance : bool
If True, normalize covariances by N-1 rather than, N where N is the number of pixels within the sliding window.
K1 : float
Algorithm parameter, K1 (small constant, see [R409]).
K2 : float
Algorithm parameter, K2 (small constant, see [R409]).
sigma : float
Standard deviation for the Gaussian when gaussian_weights is True.
Notes
To match the implementation of Wang et. al. [R409], 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
- R409(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
- R410(1,2)
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
Examples using skimage.metrics.structural_similarity
¶
variation_of_information¶
-
skimage.metrics.
variation_of_information
(image0=None, image1=None, *, table=None, ignore_labels=())[source]¶ Return symmetric conditional entropies associated with the VI. [R411]
The variation of information is defined as VI(X,Y) = H(X|Y) + H(Y|X). If X is the ground-truth segmentation, then H(X|Y) can be interpreted as the amount of under-segmentation and H(X|Y) as the amount of over-segmentation. In other words, a perfect over-segmentation will have H(X|Y)=0 and a perfect under-segmentation will have H(Y|X)=0.
- Parameters
image0, image1 : ndarray of int
Label images / segmentations, must have same shape.
table : scipy.sparse array in csr format, optional
A contingency table built with skimage.evaluate.contingency_table. If None, it will be computed with skimage.evaluate.contingency_table. If given, the entropies will be computed from this table and any images will be ignored.
ignore_labels : sequence of int, optional
Labels to ignore. Any part of the true image labeled with any of these values will not be counted in the score.
- Returns
vi : ndarray of float, shape (2,)
The conditional entropies of image1|image0 and image0|image1.
References
- R411(1,2)
Marina Meilă (2007), Comparing clusterings—an information based distance, Journal of Multivariate Analysis, Volume 98, Issue 5, Pages 873-895, ISSN 0047-259X, DOI:10.1016/j.jmva.2006.11.013.