topostats.tracing.skeletonize

Skeletonize molecules.

Attributes

LOGGER

Classes

getSkeleton	Class skeletonising images.
topostatsSkeletonize	Skeletonise a binary array following Zhang's algorithm (Zhang and Suen, 1984).

Module Contents

topostats.tracing.skeletonize.LOGGER

class topostats.tracing.skeletonize.getSkeleton(image: numpy.typing.NDArray, mask: numpy.typing.NDArray, method: str = 'zhang', height_bias: float = 0.6)

Class skeletonising images.

Parameters:

• image (npt.NDArray) – Image used to generate the mask.

• mask (npt.NDArray) – Binary mask of features.

• method (str) – Method for skeletonizing. Options ‘zhang’ (default), ‘lee’, ‘medial_axis’, ‘thin’ and ‘topostats’.

• height_bias (float) – Ratio of lowest intensity (height) pixels to total pixels fitting the skeletonisation criteria. 1 is all pixels smiilar to Zhang.

image

mask

method

height_bias

get_skeleton() → numpy.typing.NDArray

Skeletonise molecules.

Returns:

Skeletonised version of the binary mask (possibly using criteria from the image).

Return type:

npt.NDArray

_get_skeletonize() → collections.abc.Callable

Determine which skeletonise method to use.

Returns:

Returns the function appropriate for the required skeletonizing method.

Return type:

Callable

static _skeletonize_zhang(mask: numpy.typing.NDArray) → numpy.typing.NDArray

Use scikit-image implementation of the Zhang skeletonisation method.

Parameters:

mask (npt.NDArray) – Binary array to skeletonise.

Returns:

Mask array reduced to a single pixel thickness.

Return type:

npt.NDArray

static _skeletonize_lee(mask: numpy.typing.NDArray) → numpy.typing.NDArray

Use scikit-image implementation of the Lee skeletonisation method.

Parameters:

mask (npt.NDArray) – Binary array to skeletonise.

Returns:

Mask array reduced to a single pixel thickness.

Return type:

npt.NDArray

static _skeletonize_medial_axis(mask: numpy.typing.NDArray) → numpy.typing.NDArray

Use scikit-image implementation of the Medial axis skeletonisation method.

Parameters:

mask (npt.NDArray) – Binary array to skeletonise.

Returns:

Mask array reduced to a single pixel thickness.

Return type:

npt.NDArray

static _skeletonize_thin(mask: numpy.typing.NDArray) → numpy.typing.NDArray

Use scikit-image implementation of the thinning skeletonisation method.

Parameters:

mask (npt.NDArray) – Binary array to skeletonise.

Returns:

Mask array reduced to a single pixel thickness.

Return type:

npt.NDArray

static _skeletonize_topostats(image: numpy.typing.NDArray, mask: numpy.typing.NDArray, height_bias: float = 0.6) → numpy.typing.NDArray

Use scikit-image implementation of the Zhang skeletonisation method.

This method is based on Zhang’s method but produces different results (less branches but slightly less accurate).

Parameters:

• image (npt.NDArray) – Original image with heights.

• mask (npt.NDArray) – Binary array to skeletonise.

• height_bias (float) – Ratio of lowest intensity (height) pixels to total pixels fitting the skeletonisation criteria. 1 is all pixels smiilar to Zhang.

Returns:

Masked array reduced to a single pixel thickness.

Return type:

npt.NDArray

class topostats.tracing.skeletonize.topostatsSkeletonize(image: numpy.typing.NDArray, mask: numpy.typing.NDArray, height_bias: float = 0.6)

Skeletonise a binary array following Zhang’s algorithm (Zhang and Suen, 1984).

Modifications are made to the published algorithm during the removal step to remove a fraction of the smallest pixel values opposed to all of them in the aforementioned algorithm. All operations are performed on the mask entered.

Parameters:

• image (npt.NDArray) – Original 2D image containing the height data.

• mask (npt.NDArray) – Binary image containing the object to be skeletonised. Dimensions should match those of ‘image’.

• height_bias (float) – Ratio of lowest intensity (height) pixels to total pixels fitting the skeletonisation criteria. 1 is all pixels smiilar to Zhang.

image

mask

height_bias

skeleton_converged = False

p2 = None

p3 = None

p4 = None

p5 = None

p6 = None

p7 = None

p8 = None

p9 = None

counter = 0

do_skeletonising() → numpy.typing.NDArray

Perform skeletonisation.

Returns:

The single pixel thick, skeletonised array.

Return type:

npt.NDArray

_do_skeletonising_iteration() → None

Obtain the local binary pixel environment and assess the local pixel values.

This determines whether to delete a point according to the Zhang algorithm.

Then removes ratio of lowest intensity (height) pixels to total pixels fitting the skeletonisation criteria. 1 is all pixels smiilar to Zhang.

_delete_pixel_subit1(point: list) → bool

Check whether a single point (P1) should be deleted based on its local binary environment.

1. 2 ≤ B(P1) ≤ 6, where B(P1) is the number of non-zero neighbours of P1.

(b) A(P1) = 1, where A(P1) is the # of 01’s around P1. (C) P2 * P4 * P6 = 0 (d) P4 * P6 * P8 = 0

Parameters:

point (list) – List of [x, y] coordinate positions.

Returns:

Indicates whether to delete depending on whether the surrounding points have met the criteria of the binary thin a, b returncount, c and d checks below.

Return type:

bool

_delete_pixel_subit2(point: list) → bool

Check whether a single point (P1) should be deleted based on its local binary environment.

1. 2 ≤ B(P1) ≤ 6, where B(P1) is the number of non-zero neighbours of P1.

(b) A(P1) = 1, where A(P1) is the # of 01’s around P1. (c’) P2 * P4 * P8 = 0 (d’) P2 * P6 * P8 = 0

Parameters:

point (list) – List of [x, y] coordinate positions.

Returns:

Whether surrounding points have met the criteria of the binary thin a, b returncount, csharp and dsharp checks below.

Return type:

bool

_binary_thin_check_a() → bool

Check the surrounding area to see if the point lies on the edge of the grain.

Condition A protects the endpoints (which will be < 2)

Returns:

If point lies on edge of graph and isn’t an endpoint.

Return type:

bool

_binary_thin_check_b_returncount() → int

Count local area 01’s in order around P1.

??? What does this mean?

Returns:

The number of 01’s around P1.

Return type:

int

_binary_thin_check_c() → bool

Check if p2, p4 or p6 is 0.

Returns:

If p2, p4 or p6 is 0.

Return type:

bool

_binary_thin_check_d() → bool

Check if p4, p6 or p8 is 0.

Returns:

If p4, p6 or p8 is 0.

Return type:

bool

_binary_thin_check_csharp() → bool

Check if p2, p4 or p8 is 0.

Returns:

If p2, p4 or p8 is 0.

Return type:

bool

_binary_thin_check_dsharp() → bool

Check if p2, p6 or p8 is 0.

Returns:

If p2, p6 or p8 is 0.

Return type:

bool

final_skeletonisation_iteration() → None

Remove “hanging” pixels.

Examples of such pixels are:

[0, 0, 0] [0, 1, 0] [0, 0, 0] [0, 1, 1] [0, 1, 1] [0, 1, 1]

case 1: [0, 1, 0] or case 2: [0, 1, 0] or case 3: [1, 1, 0]

This is useful for the future functions that rely on local pixel environment to make assessments about the overall shape/structure of traces.

_binary_final_thin_check_a() → bool

Assess if local area has 4-connectivity.

Returns:

Logical indicator of whether if any neighbours of the 4-connections have a near pixel.

Return type:

bool

_binary_final_thin_check_b() → bool

Assess if local area 4-connectivity is connected to multiple branches.

Returns:

Logical indicator of whether if any neighbours of the 4-connections have a near pixel.

Return type:

bool

binary_thin_check_diag() → bool

Check if opposite corner diagonals are present.

Returns:

Whether a diagonal exists.

Return type:

bool

static get_local_pixels_binary(binary_map: numpy.typing.NDArray, x: int, y: int) → numpy.typing.NDArray

Value of pixels in the local 8-connectivity area around the coordinate (P1) described by x and y.

P1 must not lie on the edge of the binary map.

[[p7, p8, p9], [[0,1,2],

[p6, P1, p2], -> [3,4,5], -> [0,1,2,3,5,6,7,8] [p5, p4, p3]] [6,7,8]]

delete P1 to only get local area.

Parameters:

• binary_map (npt.NDArray) – Binary mask of image.

• x (int) – X coordinate within the binary map.

• y (int) – Y coordinate within the binary map.

Returns:

Flattened 8-long array describing the values in the binary map around the x,y point.

Return type:

npt.NDArray

static sort_and_shuffle(arr: numpy.typing.NDArray, seed: int = 23790101) → tuple[numpy.typing.NDArray, numpy.typing.NDArray]

Sort array in ascending order and shuffle the order of identical values are the same.

Parameters:

• arr (npt.NDArray) – A flattened (1D) array.

• seed (int) – Seed for random number generator.

Returns:

• npt.NDArray – An ascending order array where identical value orders are also shuffled.

• npt.NDArray – An ascending order index array of above where identical value orders are also shuffled.