gala.evaluate: Segmentation evaluation¶

gala.evaluate.adapted_rand_error(seg, gt, all_stats=False)[source]¶

Compute Adapted Rand error as defined by the SNEMI3D contest [1]

Formula is given as 1 - the maximal F-score of the Rand index (excluding the zero component of the original labels). Adapted from the SNEMI3D MATLAB script, hence the strange style.

Parameters:

seg : np.ndarray

the segmentation to score, where each value is the label at that point

gt : np.ndarray, same shape as seg

the groundtruth to score against, where each value is a label

all_stats : boolean, optional

whether to also return precision and recall as a 3-tuple with rand_error

Returns:

are : float

The adapted Rand error; equal to $1 -

rac{2pr}{p + r}$,

where $p$ and $r$ are the precision and recall described below.

prec : float, optional

The adapted Rand precision. (Only returned when all_stats is True.)

rec : float, optional

The adapted Rand recall. (Only returned when all_stats is True.)

gala.evaluate.adj_rand_index(x, y=None)[source]¶

Return the adjusted Rand index.

The Adjusted Rand Index (ARI) is the deviation of the Rand Index from the expected value if the marginal distributions of the contingency table were independent. Its value ranges from 1 (perfectly correlated marginals) to -1 (perfectly anti-correlated).

Parameters:

x, y : np.ndarray

Either x and y are provided as equal-shaped np.ndarray label fields (int type), or y is not provided and x is a contingency table (sparse.csc_matrix) that is not normalised to sum to 1.

Returns:

ari : float

The adjusted Rand index of x and y.

gala.evaluate.assignment_table(seg_or_ctable, gt=None, *, dtype=<class 'numpy.bool_'>)[source]¶

Create an assignment table of value in seg to gt.

Parameters:

seg_or_ctable : array of int, or 2D array of float

The segmentation to assign. Every value in seg will be assigned to a single value in gt. Alternatively, pass a single, pre-computed contingency table to be converted to an assignment table.

gt : array of int, same shape as seg

The segmentation to assign to. Don’t pass if seg_or_cont is a contingency matrix.

dtype : numpy dtype specification

The desired data type for the assignment matrix.

Returns:

assignments : sparse matrix

A matrix with True at position [i, j] if segment i in seg is assigned to segment j in gt.

Examples

>>> seg = np.array([0, 1, 1, 1, 2, 2])
>>> gt = np.array([1, 1, 1, 2, 2, 2])
>>> assignment_table(seg, gt).toarray()
array([[False,  True, False],
       [False,  True, False],
       [False, False,  True]], dtype=bool)
>>> cont = contingency_table(seg, gt)
>>> assignment_table(cont).toarray()
array([[False,  True, False],
       [False,  True, False],
       [False, False,  True]], dtype=bool)

gala.evaluate.contingency_table(seg, gt, *, ignore_seg=(), ignore_gt=(), norm=True)[source]¶

Return the contingency table for all regions in matched segmentations.

Parameters:

seg : np.ndarray, int type, arbitrary shape

A candidate segmentation.

gt : np.ndarray, int type, same shape as seg

The ground truth segmentation.

ignore_seg : iterable of int, optional

Values to ignore in seg. Voxels in seg having a value in this list will not contribute to the contingency table. (default: [0])

ignore_gt : iterable of int, optional

Values to ignore in gt. Voxels in gt having a value in this list will not contribute to the contingency table. (default: [0])

norm : bool, optional

Whether to normalize the table so that it sums to 1.

Returns:

cont : scipy.sparse.csr_matrix

A contingency table. cont[i, j] will equal the number of voxels labeled i in seg and j in gt. (Or the proportion of such voxels if norm=True.)

class gala.evaluate.csrRowExpandableCSR(arg1, shape=None, dtype=None, copy=False, max_num_rows=None, max_nonzero=None, expansion_factor=2)[source]¶

Like a scipy CSR matrix, but rows can be appended.

Use mat[i] = v to append the row-vector v as row i to the matrix mat. Any rows between the current last row and i are filled with zeros.

Parameters:

arg1 :

Any valid instantiation of a sparse.csr_matrix. This includes a dense matrix or 2D NumPy array, any SciPy sparse matrix, or a tuple of the three defining values of a scipy sparse matrix, (data, indices, indptr). See the documentation for sparse.csr_matrix for more information.

dtype : numpy dtype specification, optional

The data type contained in the matrix, e.g. ‘float32’, np.float64, np.complex128.

shape : tuple of two ints, optional

The number of rows and columns of the matrix.

copy : bool, optional

This argument does nothing, and is maintained for compatibility with the csr_matrix constructor. Because we create bigger-than- necessary buffer arrays, the data must always be copied.

max_num_rows : int, optional

The initial maximum number of rows. Note that more rows can always be added; this is used only for efficiency. If None, defaults to twice the initial number of rows.

max_nonzero : int, optional

The maximum number of nonzero elements. As with max_num_rows, this is only necessary for efficiency.

expansion_factor : int or float, optional

The maximum number of rows or nonzero elements will be this number times the initial number of rows or nonzero elements. This is overridden if max_num_rows or max_nonzero are provided.

Examples

>>> init = csrRowExpandableCSR([[0, 0, 2], [0, 4, 0]])
>>> init[2] = np.array([9, 0, 0])
>>> init[4] = sparse.csr_matrix([0, 0, 5])
>>> init.nnz
4
>>> init.data
array([2, 4, 9, 5], dtype=int64)
>>> init.toarray()
array([[0, 0, 2],
       [0, 4, 0],
       [9, 0, 0],
       [0, 0, 0],
       [0, 0, 5]], dtype=int64)

Attributes

Methods

data¶: The data array is virtual, truncated from the data “buffer”, _data.

gala.evaluate.divide_columns(matrix, row, in_place=False)[source]¶

Divide each column of matrix by the corresponding element in row.

The result is as follows: out[i, j] = matrix[i, j] / row[j]

Parameters:

matrix : np.ndarray, scipy.sparse.csc_matrix or csr_matrix, shape (M, N)

The input matrix.

column : a 1D np.ndarray, shape (N,)

The row dividing matrix.

in_place : bool (optional, default False)

Do the computation in-place.

Returns:

out : same type as matrix

The result of the row-wise division.

gala.evaluate.divide_rows(matrix, column, in_place=False)[source]¶

Divide each row of matrix by the corresponding element in column.

The result is as follows: out[i, j] = matrix[i, j] / column[i]

Parameters:

matrix : np.ndarray, scipy.sparse.csc_matrix or csr_matrix, shape (M, N)

The input matrix.

column : a 1D np.ndarray, shape (M,)

The column dividing matrix.

in_place : bool (optional, default False)

Do the computation in-place.

Returns:

out : same type as matrix

The result of the row-wise division.

gala.evaluate.edit_distance(aseg, gt, size_threshold=1000, sp=None)[source]¶

Find the number of splits and merges needed to convert aseg to gt.

Parameters:

aseg : np.ndarray, int type, arbitrary shape

The candidate automatic segmentation being evaluated.

gt : np.ndarray, int type, same shape as aseg

The ground truth segmentation.

size_threshold : int or float, optional

Ignore splits or merges smaller than this number of voxels.

sp : np.ndarray, int type, same shape as aseg, optional

A superpixel map. If provided, compute the edit distance to the best possible agglomeration of sp to gt, rather than to gt itself.

Returns:

(false_merges, false_splits) : float

The number of splits and merges needed to convert aseg to gt.

gala.evaluate.fm_index(x, y=None)[source]¶

Return the Fowlkes-Mallows index. [1]

Parameters:

x, y : np.ndarray

Either x and y are provided as equal-shaped np.ndarray label fields (int type), or y is not provided and x is a contingency table (sparse.csc_matrix) that is not normalised to sum to 1.

Returns:

fm : float

The FM index of x and y. 1 is perfect agreement.

References

[1] EB Fowlkes & CL Mallows. (1983) A method for comparing two hierarchical clusterings. J Am Stat Assoc 78: 553

gala.evaluate.get_stratified_sample(ar, n)[source]¶

Get a regularly-spaced sample of the unique values of an array.

Parameters:

ar : np.ndarray, arbitrary shape and type

The input array.

n : int

The desired sample size.

Returns:

u : np.ndarray, shape approximately (n,)

Notes

If len(np.unique(ar)) <= 2*n, all the values of ar are returned. The requested sample size is taken as an approximate lower bound.

Examples

>>> ar = np.array([[0, 4, 1, 3],
...                [4, 1, 3, 5],
...                [3, 5, 2, 1]])
>>> np.unique(ar)
array([0, 1, 2, 3, 4, 5])
>>> get_stratified_sample(ar, 3)
array([0, 2, 4])

gala.evaluate.make_synaptic_functions(fn, fcts)[source]¶

Make evaluation functions that only evaluate at synaptic sites.

Parameters:

fn : string

Filename containing synapse coordinates, in Raveler format. [1]

fcts : function, or iterable of functions

Functions to be converted to synaptic evaluation.

Returns:

syn_fcts : function or iterable of functions

Evaluation functions that will evaluate only at synaptic sites.

Raises:

ImportError : if the syngeo package [2, 3] is not installed.

References

[1] https://wiki.janelia.org/wiki/display/flyem/synapse+annotation+file+format [2] https://github.com/janelia-flyem/synapse-geometry [3] https://github.com/jni/synapse-geometry

gala.evaluate.make_synaptic_vi(fn)[source]¶: Shortcut for make_synaptic_functions(fn, split_vi).

gala.evaluate.merge_contingency_table(a, b, ignore_seg=[0], ignore_gt=[0])[source]¶

A contingency table that has additional rows for merging initial rows.

Parameters:

a

b

ignore_seg

ignore_gt

Returns:

ct : array, shape (2M + 1, N)

gala.evaluate.nzcol(mat, row_idx)[source]¶

Return the nonzero elements of given row in a CSR matrix.

Parameters:

mat : CSR matrix

Input matrix.

row_idx : int

The index of the row (if mat is CSR) for which the nonzero elements are desired.

Returns:

nz : array of int

The location of nonzero elements of mat[main_axis_idx].

Examples

>>> mat = sparse.csr_matrix(np.array([[0, 1, 0, 0], [0, 5, 8, 0]]))
>>> nzcol(mat, 1)
array([1, 2], dtype=int32)
>>> mat[1, 2] = 0
>>> nzcol(mat, 1)
array([1], dtype=int32)

gala.evaluate.pixel_wise_boundary_precision_recall(pred, gt)[source]¶

Evaluate voxel prediction accuracy against a ground truth.

Parameters:

pred : np.ndarray of int or bool, arbitrary shape

The voxel-wise discrete prediction. 1 for boundary, 0 for non-boundary.

gt : np.ndarray of int or bool, same shape as pred

The ground truth boundary voxels. 1 for boundary, 0 for non-boundary.

Returns:

pr : float

rec : float

The precision and recall values associated with the prediction.

Notes

Precision is defined as “True Positives / Total Positive Calls”, and Recall is defined as “True Positives / Total Positives in Ground Truth”.

This function only calculates this value for discretized predictions, i.e. it does not work with continuous prediction confidence values.

gala.evaluate.rand_by_threshold(ucm, gt, npoints=None)[source]¶

Compute Rand and Adjusted Rand indices for each threshold of a UCM

Parameters:

ucm : np.ndarray, arbitrary shape

An Ultrametric Contour Map of region boundaries having specific values. Higher values indicate higher boundary probabilities.

gt : np.ndarray, int type, same shape as ucm

The ground truth segmentation.

npoints : int, optional

If provided, only compute values at npoints thresholds, rather than all thresholds. Useful when ucm has an extremely large number of unique values.

Returns:

ris : np.ndarray of float, shape (3, len(np.unique(ucm))) or (3, npoints)

The rand indices of the segmentation induced by thresholding and labeling ucm at different values. The 3 rows of ris are the values used for thresholding, the corresponding Rand Index at that threshold, and the corresponding Adjusted Rand Index at that threshold.

gala.evaluate.rand_index(x, y=None)[source]¶

Return the unadjusted Rand index. [1]

Parameters:

x, y : np.ndarray

Either x and y are provided as equal-shaped np.ndarray label fields (int type), or y is not provided and x is a contingency table (sparse.csc_matrix) that is not normalised to sum to 1.

Returns:

ri : float

The Rand index of x and y.

References

[1] WM Rand. (1971) Objective criteria for the evaluation of clustering methods. J Am Stat Assoc. 66: 846–850

gala.evaluate.rand_values(cont_table)[source]¶

Calculate values for Rand Index and related values, e.g. Adjusted Rand.

Parameters:

cont_table : scipy.sparse.csc_matrix

A contingency table of the two segmentations.

Returns:

a, b, c, d : float

The values necessary for computing Rand Index and related values. [1, 2]

a : float

Refers to the number of pairs of elements in the input image that are both the same in seg1 and in seg2,

b : float

Refers to the number of pairs of elements in the input image that are different in both seg1 and in seg2.

c : float

Refers to the number of pairs of elements in the input image that are the same in seg1 but different in seg2.

d : float

Refers to the number of pairs of elements in the input image that are different in seg1 but the same in seg2.

References

[1] Rand, W. M. (1971). Objective criteria for the evaluation of clustering methods. J Am Stat Assoc. [2] http://en.wikipedia.org/wiki/Rand_index#Definition on 2013-05-16.

gala.evaluate.raw_edit_distance(aseg, gt, size_threshold=1000)[source]¶

Compute the edit distance between two segmentations.

Parameters:

aseg : np.ndarray, int type, arbitrary shape

The candidate automatic segmentation.

gt : np.ndarray, int type, same shape as aseg

The ground truth segmentation.

size_threshold : int or float, optional

Ignore splits or merges smaller than this number of voxels.

Returns:

(false_merges, false_splits) : float

The number of splits and merges required to convert aseg to gt.

gala.evaluate.reduce_vi(fn_pattern='testing/%i/flat-single-channel-tr%i-%i-%.2f.lzf.h5', iterable=[(0, 1, 0), (0, 2, 0), (0, 3, 0), (0, 4, 0), (0, 5, 0), (0, 6, 0), (0, 7, 0), (1, 0, 1), (1, 2, 1), (1, 3, 1), (1, 4, 1), (1, 5, 1), (1, 6, 1), (1, 7, 1), (2, 0, 2), (2, 1, 2), (2, 3, 2), (2, 4, 2), (2, 5, 2), (2, 6, 2), (2, 7, 2), (3, 0, 3), (3, 1, 3), (3, 2, 3), (3, 4, 3), (3, 5, 3), (3, 6, 3), (3, 7, 3), (4, 0, 4), (4, 1, 4), (4, 2, 4), (4, 3, 4), (4, 5, 4), (4, 6, 4), (4, 7, 4), (5, 0, 5), (5, 1, 5), (5, 2, 5), (5, 3, 5), (5, 4, 5), (5, 6, 5), (5, 7, 5), (6, 0, 6), (6, 1, 6), (6, 2, 6), (6, 3, 6), (6, 4, 6), (6, 5, 6), (6, 7, 6), (7, 0, 7), (7, 1, 7), (7, 2, 7), (7, 3, 7), (7, 4, 7), (7, 5, 7), (7, 6, 7)], thresholds=array([0. , 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1 , 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2 , 0.21, 0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3 , 0.31, 0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4 , 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5 , 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6 , 0.61, 0.62, 0.63, 0.64, 0.65, 0.66, 0.67, 0.68, 0.69, 0.7 , 0.71, 0.72, 0.73, 0.74, 0.75, 0.76, 0.77, 0.78, 0.79, 0.8 , 0.81, 0.82, 0.83, 0.84, 0.85, 0.86, 0.87, 0.88, 0.89, 0.9 , 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99, 1. ]))[source]¶

Compile evaluation results embedded in many .h5 files under “vi”.

Parameters:

fn_pattern : string, optional

A format string defining the files to be examined.

iterable : iterable of tuples, optional

The (partial) tuples to apply to the format string to obtain individual files.

thresholds : iterable of float, optional

The final tuple elements to apply to the format string. The final tuples are the product of iterable and thresholds.

Returns:

vi : np.ndarray of float, shape (3, len(thresholds))

The under and over segmentation components of VI at each threshold. vi[0, :] is the threshold, vi[1, :] the undersegmentation and vi[2, :] is the oversegmentation.

gala.evaluate.relabel_from_one(label_field)[source]¶

Convert labels in an arbitrary label field to {1, … number_of_labels}.

This function also returns the forward map (mapping the original labels to the reduced labels) and the inverse map (mapping the reduced labels back to the original ones).

Parameters:

label_field : numpy ndarray (integer type)

Returns:

relabeled : numpy array of same shape as ar

forward_map : 1d numpy array of length np.unique(ar) + 1

inverse_map : 1d numpy array of length len(np.unique(ar))

The length is len(np.unique(ar)) + 1 if 0 is not in np.unique(ar)

Examples

>>> import numpy as np
>>> label_field = np.array([1, 1, 5, 5, 8, 99, 42])
>>> relab, fw, inv = relabel_from_one(label_field)
>>> relab
array([1, 1, 2, 2, 3, 5, 4])
>>> fw
array([0, 1, 0, 0, 0, 2, 0, 0, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 4, 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, 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, 0, 0, 0, 0, 0, 0, 5])
>>> inv
array([ 0,  1,  5,  8, 42, 99])
>>> (fw[label_field] == relab).all()
True
>>> (inv[relab] == label_field).all()
True

gala.evaluate.sem(ar, axis=None)[source]¶

Calculate the standard error of the mean (SEM) along an axis.

Parameters:

ar : np.ndarray

The input array of values.

axis : int, optional

Calculate SEM along the given axis. If omitted, calculate along the raveled array.

Returns:

sem : float or np.ndarray of float

The SEM over the whole array (if axis=None) or over the chosen axis.

gala.evaluate.sorted_vi_components(s1, s2, ignore1=[0], ignore2=[0], compress=False)[source]¶

Return lists of the most entropic segments in s1|s2 and s2|s1.

Parameters:

s1, s2 : np.ndarray of int

Segmentations to be compared. Usually, s1 will be a candidate segmentation and s2 will be the ground truth or target segmentation.

ignore1, ignore2 : list of int, optional

Labels in these lists are ignored in computing the VI. 0-labels are ignored by default; pass empty lists to use all labels.

compress : bool, optional

The ‘compress’ flag performs a remapping of the labels before doing the VI computation, resulting in memory savings when many labels are not used in the volume. (For example, if you have just two labels, 1 and 1,000,000, ‘compress=False’ will give a vector of length 1,000,000, whereas with ‘compress=True’ it will have just size 2.)

Returns:

ii1 : np.ndarray of int

The labels in s2 having the most entropy. If s1 is the automatic segmentation, these are the worst false merges.

h2g1 : np.ndarray of float

The conditional entropy corresponding to the labels in ii1.

ii2 : np.ndarray of int (seg)

The labels in s1 having the most entropy. These correspond to the worst false splits.

h2g1 : np.ndarray of float

The conditional entropy corresponding to the labels in ii2.

gala.evaluate.special_points_evaluate(eval_fct, coords, flatten=True, coord_format=True)[source]¶

Return an evaluation function to only evaluate at special coordinates.

Parameters:

eval_fct : function taking at least two np.ndarray of equal shapes as args

The function to be used for evaluation.

coords : np.ndarray of int, shape (n_points, n_dim) or (n_points,)

The coordinates at which to evaluate the function. The coordinates can either be subscript format (one index into each dimension of input arrays) or index format (a single index into the linear array). For the latter, use flatten=False.

flatten : bool, optional

Whether to flatten the coordinates (default) or leave them untouched (if they are already in raveled format).

coord_format : bool, optional

Format the coordinates to a tuple of np.ndarray as numpy expects. Set to False if coordinates are already in this format or flattened.

Returns:

special_eval_fct : function taking at least two np.ndarray of equal shapes

The returned function is the same as the above function but only evaluated at the coordinates specified. This can be used, for example, to subsample a volume, or to evaluate only whether synapses are correctly assigned, rather than every voxel, in a neuronal image volume.

gala.evaluate.split_components(idx, cont, num_elems=4, axis=0)[source]¶

Return the indices of the bodies most overlapping with body idx.

Parameters:

idx : int

The segment index being examined.

cont : sparse.csc_matrix

The normalized contingency table.

num_elems : int, optional

The number of overlapping bodies desired.

axis : int, optional

The axis along which to perform the calculations. Assuming cont has the automatic segmentation as the rows and the gold standard as the columns, axis=0 will return the segment IDs in the gold standard of the worst merges comprising idx, while axis=1 will return the segment IDs in the automatic segmentation of the worst splits comprising idx.

Value:

comps : list of (int, float, float) tuples

num_elems indices of the biggest overlaps comprising idx, along with the percent of idx that they comprise and the percent of themselves that overlaps with idx.

gala.evaluate.split_vi(x, y=None, ignore_x=[0], ignore_y=[0])[source]¶

Return the symmetric conditional entropies associated with the VI.

The variation of information is defined as VI(X,Y) = H(X|Y) + H(Y|X). If Y is the ground-truth segmentation, then H(Y|X) can be interpreted as the amount of under-segmentation of Y and H(X|Y) is then the amount of over-segmentation. In other words, a perfect over-segmentation will have H(Y|X)=0 and a perfect under-segmentation will have H(X|Y)=0.

If y is None, x is assumed to be a contingency table.

Parameters:

x : np.ndarray

Label field (int type) or contingency table (float). x is interpreted as a contingency table (summing to 1.0) if and only if y is not provided.

y : np.ndarray of int, same shape as x, optional

A label field to compare to x.

ignore_x, ignore_y : list of int, optional

Any points having a label in this list are ignored in the evaluation. Ignore 0-labeled points by default.

Returns:

sv : np.ndarray of float, shape (2,)

The conditional entropies of Y|X and X|Y.