# Algorithms¶

## Fragment Generation¶

class brainlit.algorithms.generate_fragments.state_generation(image_path: str, ilastik_program_path: str, ilastik_project_path: str, chunk_size: List[float] = [375, 375, 125], soma_coords: List[list] = [], resolution: List[float] = [0.3, 0.3, 1], parallel: int = 1, prob_path: str = None, fragment_path: str = None, tiered_path: str = None, states_path: str = None)[source]
compute_bfs(self)[source]

Compute bfs from highest degree node

compute_edge_weights(self)[source]

Create viterbrain object and compute edge weights

compute_frags(self)[source]

Compute all fragments for image

compute_image_tiered(self)[source]

Compute entire tiered image then reassemble and save as zarr

compute_soma_lbls(self)[source]

Compute fragment ids of soma coordinates.

compute_states(self)[source]

Compute entire collection of states

Raises

ValueError -- erroneously computed endpoints of soma state

predict(self, data_bin: str)[source]

Run ilastik on zarr image

Parameters

data_bin (str) -- path to directory to store intermediate files

brainlit.algorithms.generate_fragments.get_seed(voxel)[source]

Get a seed point for the center of a brain volume.

Parameters

voxel (tuple:) -- The seed coordinates in x y z.

Returns

A tuple containing the (x, y, z)-coordinates of the seed.

Return type

tuple

brainlit.algorithms.generate_fragments.get_img_T1(img)[source]

Converts a volume cutout to a SimpleITK image, as wel as a SimpleITK image with scaled intensity values to 0-255.

Parameters

img (cloudvolume.volumecutout.VolumeCutout) -- The volume to convert to a SimpleITK image.

Returns

• img_T1 (SimpleITK.SimpleITK.Image) -- A SimpleITK image.

• img_T1_255 (SimpleITK.SimpleITK.Image) -- A SimpleITK image with intensity values between 0 and 255 inclusive.

brainlit.algorithms.generate_fragments.thres_from_gmm(img, random_seed=2)[source]

Computes a numerical threshold for segmentation based on a 2-Component Gaussian mixture model.

The threshold is the minimum value included in the Gaussian mixture model-component containning the highest intensity value.

Parameters
• img (cloudvolume.volumecutout.VolumeCutout) -- The image or volume to threshold.

• random_seed (int) -- The random seed for the Gaussian mixture model.

Returns

The threshold value.

Return type

int

brainlit.algorithms.generate_fragments.fast_marching_seg(img, seed, stopping_value=150, sigma=0.5)[source]

Computes a fast-marching segmentation.

Parameters
• img (cloudvolume.volumecutout.VolumeCutout) -- The volume to segment.

• seed (tuple) -- The seed containing a coordinate within a known segment.

• stopping_value (float) -- The algorithm stops when the value of the smallest trial point is greater than this stopping value.

• sigma (float) -- Sigma used in computing the feature image.

Returns

labels -- An array consisting of the pixelwise segmentation.

Return type

numpy.ndarray

brainlit.algorithms.generate_fragments.level_set_seg(img, seed, lower_threshold=None, upper_threshold=None, factor=2, max_rms_error=0.02, num_iter=1000, curvature_scaling=0.5, propagation_scaling=1)[source]

Computes a level-set segmentation.

When root mean squared change in the level set function for an iteration is below the threshold, or the maximum number of iteration have elapsed, the algorithm is said to have converged.

Parameters
• img (cloudvolume.volumecutout.VolumeCutout) -- The volume to segment.

• seed (tuple) -- The seed containing a coordinate within a known segment.

• lower_threshold (float) -- The lower threshold for segmentation. Set based on image statistics if None.

• upper_threshold (float) -- The upper threshold for segmentation. Set based on image statistics if None.

• factor (float) -- The scaling factor on the standard deviation used in computing thresholds from image statistics.

• max_rms_error (float) -- Root mean squared convergence criterion threshold.

• num_iter (int) -- Maximum number of iterations.

• curvature_scaling (float) -- Curvature scaling for the segmentation.

• propagation_scaling (float) -- Propagation scaling for the segmentation.

Returns

labels -- An array consisting of the pixelwise segmentation.

Return type

numpy.ndarray

brainlit.algorithms.generate_fragments.connected_threshold(img, seed, lower_threshold=None, upper_threshold=255)[source]

Compute a threshold-based segmentation via connected region growing.

Labelled pixels are connected to a seed and lie within a range of values.

Parameters
• img (cloudvolume.volumecutout.VolumeCutout) -- The volume to segment.

• seed (tuple) -- The seed containing a coordinate within a known segment.

• lower_threshold (float) -- The lower threshold for the region growth. Set by a 2-component Gaussian mixture model if None.

• upper_threshold (float) -- The upper threshold for the region growth.

Returns

labels -- An array consisting of the pixelwise segmentation.

Return type

numpy.ndarray

brainlit.algorithms.generate_fragments.confidence_connected_threshold(img, seed, num_iter=1, multiplier=1, initial_neighborhood_radius=1, replace_value=1)[source]

Compute a threshold-based segmentation via confidence-connected region growing.

The segmentation is based on pixels with intensities that are consistent with pixel statistics of a seed point. Pixels connected to the seed point with values within a confidence interval are grouped. The confidence interval is the mean plus of minus the "multiplier" times the standard deviation. After an initial segmentation is completed, the mean and standard deviation are calculated again at each iteration using pixels in the previous segmentation.

Parameters
• img (cloudvolume.volumecutout.VolumeCutout) -- The volume to segment.

• seed (tuple) -- The seed containing a coordinate within a known segment.

• num_iter (int) -- The number of iterations to run the algorithm.

• multiplier (float) -- Multiplier for the confidence interval.

• initial_neighborhood_radius (int) -- The initial neighborhood radius for computing statistics on the seed pixel.

• replace_value (int) -- The value to replace thresholded pixels.

Returns

labels -- An array consisting of the pixelwise segmentation.

Return type

numpy.ndarray

brainlit.algorithms.generate_fragments.neighborhood_connected_threshold(img, seed, lower_threshold=None, upper_threshold=255)[source]

Compute a threshold-based segmentation via neighborhood-connected region growing.

Labelled pixels are connected to a seed and lie within a neighborhood.

Parameters
• img (cloudvolume.volumecutout.VolumeCutout) -- The volume to segment.

• seed (tuple) -- The seed containing a coordinate within a known segment.

• lower_threshold (float) -- The lower threshold for the region growth. Set by a 2-component Gaussian mixture model if None.

• upper_threshold (float) -- The upper threshold for the region growth.

Returns

labels -- An array consisting of the pixelwise segmentation.

Return type

numpy.ndarray

brainlit.algorithms.generate_fragments.otsu(img, seed)[source]

Compute a threshold-based segmentation via Otsu's method.

Parameters

img (cloudvolume.volumecutout.VolumeCutout) -- The volume to segment.

Returns

labels -- An array consisting of the pixelwise segmentation.

Return type

numpy.ndarray

brainlit.algorithms.generate_fragments.gmm_seg(img, seed, random_seed=3)[source]

Compute a threshold-based segmentation via a 2-component Gaussian mixture model.

Parameters
• img (cloudvolume.volumecutout.VolumeCutout) -- The volume to segment.

• random_seed (int) -- The random seed for the Gaussian mixture model.

Returns

labels -- An array consisting of the pixelwise segmentation.

Return type

numpy.ndarray

## Connect Fragments¶

class brainlit.algorithms.connect_fragments.ViterBrain(G: nx.Graph, tiered_path: str, fragment_path: str, resolution: List[float], coef_curv: float, coef_dist: float, coef_int: float, parallel: int = 1)[source]
compute_all_costs_dist(self, frag_frag_func: Callable, frag_soma_func: Callable)[source]

Splits up transition computation tasks then assembles them into networkx graph

Parameters
• frag_frag_func (function) -- function that computes transition cost between fragments

• frag_soma_func (function) -- function that computes transition cost between fragments

compute_all_costs_int(self)[source]

Splits up transition computation tasks then assembles them into networkx graph

frag_frag_dist(self, pt1: List[float], orientation1: List[float], pt2: List[float], orientation2: List[float], verbose: bool = False)[source]

Compute cost of transition between two fragment states

Parameters
• pt1 (list of floats) -- first coordinate

• orientation1 (list of floats) -- orientation at first coordinate

• pt2 (list of floats) -- second coordinate

• orientation2 (list of floats) -- orientation at second coordinate

• verbose (bool, optional) -- Print transition cost information. Defaults to False.

Raises
• ValueError -- if an orientation is not unit length

• ValueError -- if distance or curvature cost is nan

Returns

cost of transition

Return type

[float]

frag_soma_dist(self, point: List[float], orientation: List[float], soma_lbl: int, verbose: bool = False)[source]

Compute cost of transition from fragment state to soma state

Parameters
• point (list of floats) -- coordinate on fragment

• orientation (list of floats) -- orientation at fragment

• soma_lbl (int) -- label of soma component

• verbose (bool, optional) -- Prints cost values. Defaults to False.

Raises
• ValueError -- if either distance or curvature cost is nan

• ValueError -- if the computed closest soma coordinate is not on the soma

Returns

cost of transition [list of floats]: closest soma coordinate

Return type

[float]

shortest_path(self, coord1: List[int], coord2: List[int])[source]

Compute coordinate path from one coordinate to another.

Parameters
• coord1 (list) -- voxel coordinate of start point

• coord2 (list) -- voxel coordinate of end point

Raises

ValueError -- if state sequence contains a soma state that is not at the end

Returns

list of voxel coordinates of path

Return type

list

## Trace Analysis¶

brainlit.algorithms.trace_analysis.speed(x: np.ndarray, t: np.ndarray, c: np.ndarray, k: np.integer, aux_outputs: bool = False)[source]

Compute the speed of a B-Spline.

The speed is the norm of the first derivative of the B-Spline.

Parameters
• x -- A 1xL array of parameter values where to evaluate the curve. It contains the parameter values where the speed of the B-Spline will be evaluated. It is required to be non-empty, one-dimensional, and real-valued.

• t -- A 1xm array representing the knots of the B-spline. It is required to be a non-empty, non-decreasing, and one-dimensional sequence of real-valued elements. For a B-Spline of degree k, at least 2k + 1 knots are required.

• c -- A dxn array representing the coefficients/control points of the B-spline. Given n real-valued, d-dimensional points ::math::x_k = (x_k(1),...,x_k(d)), c is the non-empty matrix which columns are ::math::x_1^T,...,x_N^T. For a B-Spline of order k, n cannot be less than m-k-1.

• k -- A non-negative integer representing the degree of the B-spline.

Returns

A 1xL array containing the speed of the B-Spline evaluated at x

Return type

speed

References: .. [Rbbccb9c002d5-1] Kouba, Parametric Equations.

brainlit.algorithms.trace_analysis.curvature(x: np.ndarray, t: np.ndarray, c: np.ndarray, k: np.integer, aux_outputs: bool = False)[source]

Compute the curvature of a B-Spline.

The curvature measures the failure of a curve, r(u), to be a straight line. It is defined as

$k = \lVert \frac{dT}{ds} \rVert,$

where T is the unit tangent vector, and s is the arc length:

$T = \frac{dr}{ds},\quad s = \int_0^t \lVert r'(u) \rVert du,$

where r(u) is the position vector as a function of time.

The curvature can also be computed as

$k = \lVert r'(t) \times r''(t)\rVert / \lVert r'(t) \rVert^3.$
Parameters
• x -- A 1xL array of parameter values where to evaluate the curve. It contains the parameter values where the curvature of the B-Spline will be evaluated. It is required to be non-empty, one-dimensional, and real-valued.

• t -- A 1xm array representing the knots of the B-spline. It is required to be a non-empty, non-decreasing, and one-dimensional sequence of real-valued elements. For a B-Spline of degree k, at least 2k + 1 knots are required.

• c -- A dxn array representing the coefficients/control points of the B-spline. Given n real-valued, d-dimensional points ::math::x_k = (x_k(1),...,x_k(d)), c is the non-empty matrix which columns are ::math::x_1^T,...,x_N^T. For a B-Spline of order k, n cannot be less than m-k-1.

• k -- A non-negative integer representing the degree of the B-spline.

Returns

A 1xL array containing the curvature of the B-Spline evaluated at x

Return type

curvature

References: .. [Rce97e449f49f-1] Máté Attila, The Frenet–Serret formulas.

brainlit.algorithms.trace_analysis.torsion(x: np.ndarray, t: np.ndarray, c: np.ndarray, k: np.integer, aux_outputs: bool = False)[source]

Compute the torsion of a B-Spline.

The torsion measures the failure of a curve, r(u), to be planar. If the curvature k of a curve is not zero, then the torsion is defined as

$\tau = -n \cdot b',$

where n is the principal normal vector, and b' the derivative w.r.t. the arc length s of the binormal vector.

The torsion can also be computed as

$\tau = \lvert r'(t), r''(t), r'''(t) \rvert / \lVert r'(t) \times r''(t) \rVert^2,$

where r(u) is the position vector as a function of time.

Parameters
• x -- A 1xL array of parameter values where to evaluate the curve. It contains the parameter values where the torsion of the B-Spline will be evaluated. It is required to be non-empty, one-dimensional, and real-valued.

• t -- A 1xm array representing the knots of the B-spline. It is required to be a non-empty, non-decreasing, and one-dimensional sequence of real-valued elements. For a B-Spline of degree k, at least 2k + 1 knots are required.

• c -- A dxn array representing the coefficients/control points of the B-spline. Given n real-valued, d-dimensional points ::math::x_k = (x_k(1),...,x_k(d)), c is the non-empty matrix which columns are ::math::x_1^T,...,x_N^T. For a B-Spline of order k, n cannot be less than m-k-1.

• k -- A non-negative integer representing the degree of the B-spline.

Returns

A 1xL array containing the torsion of the B-Spline evaluated at x

Return type

torsion

References: .. [R8b689f5f8f91-1] Máté Attila, The Frenet–Serret formulas.

class brainlit.algorithms.trace_analysis.GeometricGraph(df=None)[source]

The shape of the neurons are expressed and fitted with splines in this undirected graph class.

The geometry of the neurons are projected on undirected graphs, based on which the trees of neurons consisted for splines is constructed. It is required that each node has a loc attribute identifying that points location in space, and the location should be defined in 3-dimensional cartesian coordinates. It extends nx.Graph and rejects duplicate node input.

fit_spline_tree_invariant(self)[source]

Construct a spline tree based on the path lengths.

Raises
• ValueError -- check if every node is unigue in location

• ValueError -- check if every node is assigned to at least one edge

• ValueError -- check if the graph contains undirected cycle(s)

• ValueErorr -- check if the graph has disconnected segment(s)

Returns

nx.DiGraph a parent tree with the longest path in the directed graph

Return type

spline_tree

## Soma Detection¶

brainlit.algorithms.detect_somas.find_somas(volume: np.ndarray, res: list)[source]

Find bright neuron somas in an input volume.

This simple soma detector assumes that somas are brighter than the rest of the objects contained in the input volume.

To detect somas, these steps are performed:

1. Check input volume shape. This detector requires the x and y dimensions of the input volumes to be larger than 20 pixels.

2. Zoom volume. We found that this simple soma detector works best when then input volume has size 160 x 160 x 50. We use ndimage.zoom to scale the input volume size to the desired shape.

3. Binarize volume. We use Otsu thresholding to binarize the image.

4. Erode the binarized image. We erode the binarized image with a structuring element which size is directly proportional to the maximum zoom factor applied to the input volume.

5. Remove unreasonable connected components. After erosion, we compute the equivalent diameter d of each connected component, and only keep those ones such that 5mu m leq d < 21 mu m

6. Find relative centroids. Finally, we compute the centroids of the remaining connected components. The centroids are in voxel units, relative to the input volume.

Parameters
• volume (numpy.ndarray) -- The 3D image array to run the detector on.

• res (list) -- A 1 x 3 list containing the resolution of each voxel in nm.

Returns

• label (bool) -- A boolean value indicating whether the detector found any somas in the input volume.

• rel_centroids (numpy.ndarray) -- A N x 3 array containing the relative voxel positions of the detected somas.

• out (numpy.ndarray) -- A 160 x 160 x 50 array containing the detection mask.

Examples

>>> # download a volume
>>> dir = "s3://open-neurodata/brainlit/brain1"
>>> dir_segments = "s3://open-neurodata/brainlit/brain1_segments"
>>> volume_keys = "4807349.0_3827990.0_2922565.75_4907349.0_3927990.0_3022565.75"
>>> mip = 1
>>> ngl_sess = NeuroglancerSession(
>>>     mip=mip, url=dir, url_segments=dir_segments, use_https=False
>>> )
>>> res = ngl_sess.cv_segments.scales[ngl_sess.mip]["resolution"]
>>> volume_coords = np.array(os.path.basename(volume_keys).split("_")).astype(float)
>>> volume_vox_min = np.round(np.divide(volume_coords[:3], res)).astype(int)
>>> volume_vox_max = np.round(np.divide(volume_coords[3:], res)).astype(int)
>>> bbox = Bbox(volume_vox_min, volume_vox_max)
>>> img = ngl_sess.pull_bounds_img(bbox)
>>> # apply soma detector
>>> label, rel_centroids, out = find_somas(img, res)