Analysis module¶

Collection of useful analysis tools. For easy acess use the Analysis facade

Analysis facade¶

Easy access to complex algorithmic concepts.

Author:	Sebastian Reinhard
Organization:	Biophysics and Biotechnology, Julius-Maximillians-University of Würzburg
Version:	2019.06.26

impro.analysis.analysis_facade.create_alpha_shape(storm_data: numpy.ndarray, alpha_value: float, px_size=32.2, line_width=1.0) → numpy.ndarray¶

Facade function to render alpha shape of dSTORM data

Image is rendered from (0,0) to the maximal dimension of the dSTORM data.

Parameters:	storm_data (np.ndarray(nx5)) – Point Cloud data to be rendered px_size (float) – Pixel size for the rendered image in nanometer per pixel alpha_value (float) – Core value to compute the alpha shape in nanometer line_width (float) – Line width of the alpha shape lines in a.u.
Returns:	image – Rendered image
Return type:	np.array

Example

>>> points = np.random.randint(0,32000,(1000000, 2))
>>> image = create_alpha_shape(points, 130)
>>> image.shape
(994,994)

impro.analysis.analysis_facade.create_storm(storm_data: numpy.ndarray, px_size=32.2, size=20, cluster=array(3.))¶

Facade function to render an image of dSTORM data.

Image is rendered from (0,0) to the maximal dimension of the dSTORM data.

Parameters:	storm_data (np.array(nx5)) – Point Cloud data to be rendered px_size (float) – Pixel size for the rendered image in nanometer per pixel size (float) – Size of the rendered points in nanometer cluster (np.array(n)) – Affiliation of the i th point to cluster[i] cluster
Returns:	image – Rendered image
Return type:	np.array

Example

>>> points = np.random.randint(0,32000,(1000000, 5))
>>> image = create_alpha_shape(points, 130)
>>> image.shape
(994,994)

impro.analysis.analysis_facade.error_management(result_list: list, source_points, target_points, n_row=5)¶

Test the results of th weighted GHT for missmatches

Parameters:	result_list (list) – results of the Weighted General Hough Transform source_points (np.array) – Source points of affine transformation target_points (np.array) – Target points of affine transformation n_row (int) – number of rows used for the weighted GHT
Returns:	source_points, target_points – Filtered source and target points for affine transformation
Return type:	np.array

impro.analysis.analysis_facade.find_mapping(target: numpy.ndarray, source_color: numpy.ndarray, n_col=5, n_row=5, offset=0) → numpy.ndarray¶

Facade function to find a mapping from source_color image to gray scale target image.

Parameters:

target (np.array) – Target image of affine transformation
source_color (np.array) – Source image of affine transformation
n_col (int) – number of collums to seperate the source image into
n_row (int) – number of rows to seperate the source image into
offset (int) – Start seperating the source image at (0+offset,0+offset). Offset is given in pixel

Returns:

source_points, target_points (np.array) – Source and target points for affine transformation
overlay (np.array) – Target image overlayed with source image segments at the matching position
results (list) – Results of the Weighted General Hough Transform

Example

>>> import cv2
>>> points = np.random.randint(0,32000,(1000000, 5))
>>> source = create_alpha_shape(points, 130)
>>> points = np.random.randint(0,120000,(1000000, 5))
>>> target = create_alpha_shape(points, 130)
>>> find_mapping(cv2.cvtColor(target, cv2.COLOR_RGBA2GRAY), source)

impro.analysis.analysis_facade.pearson_correlation(target: numpy.ndarray, source: numpy.ndarray, map: numpy.ndarray) → float¶

Compute pearson correlation index after alignment

Parameters:	target (np.array) – target image in gray scale source (np.array) – source image in gray scale map (sklearn.transformation) – computed transformation
Returns:	source_points, target_points – Filtered source and target points for affine transformation
Return type:	np.array

Example

>>> import skimage.transform
>>> source = np.ones((1000,1000))
>>> target = np.ones((1000,1000))
>>> source_points = np.array([[1.0,1.0],[500,500],[700,500])
>>> target_points = source_points
>>> M = transform.estimate_transform("affine",source_points,target_points)
>>> pearson_correlation(target, source, M)
(1.0)

Alpha Shape¶

The objective of the alpha shape algorithm is to deliver a formal meaning for the geometric notation of ‘shape’, in the context of finite point sets. The straciatella ice cream example gives a visual explanation of the concept: Consider a ball of ice cream with chocolate pieces. The chocolate pieces represent the distribution of points in space (ice cream). The alpha shape algorithm now tries to eat as much ice cream as possible without touching any chocolate pieces, using an arbitrary predefined spoon size, the $\alpha$ -value. Choosing a very small spoon size results in all ice cream being eaten, a very big spoon size in no ice cream being eaten at all (Convex Hull). But a size in between creates a concave hull representing the shape of the distributed chocolate pieces, the desired alpha shape.

Considering the red dotted line l, the limit a is defined as the minimum of the diameter of the circumcircles around $\triangle_U$ and $\triangle_V$ . The limit b is the maximum of circumcircles around $\triangle_U$ and $\triangle_V$ . Since the $\alpha$ -ball is smaller than b, but bigger than a, l is classified as boundary.

References

Edelsbrunner, Herbert ; Mücke, Ernst P.: Three-dimensional Alpha Shapes. In: ACM Trans. Graph. 13 (1994), Januar, Nr. 1, 43–72. http: //dx.doi.org/10.1145/174462.156635. – DOI 10.1145/174462.156635. – ISSN 0730–0301
Fischer, Kaspar: Introduction to Alpha Shapes. https: //graphics.stanford.edu/courses/cs268-11-spring/handouts/ AlphaShapes/as_fisher.pdf.

Author:	Sebastian Reinhard
Organization:	Biophysics and Biotechnology, Julius-Maximillians-University of Würzburg
Version:	2018.03.09

Example

>>> data = np.random.randint(0,32000,(1000000, 2))
>>> k_simplices = get_k_simplices(data[...,0:2])[0]

class impro.analysis.alpha_shape_gpu.AlphaComplex(struct_ptr: int, indices: numpy.ndarray, points: numpy.ndarray, neighbors: numpy.ndarray)¶

Bases: object

Derive 2D alpha complex from scipy.spatial Delaunay

Class to create a alpha complex structure on GPU.

Parameters:	struct_ptr (int) – pointer to allocated memmory for structure indices (np.array) – nx3 array containing point indices of the delaunay triangulation simplices neighbors (np.array) – nx3 array containing the indices of neighboring simplices points (np.array) – nx2 array of the points used for delaunay triangulation

get()¶

Returns:	nx5 of d=1 simplices containing: [index1, index2, dist, sigma1, sigma2] with sigma 1 < sigma 2
Return type:	numpy.array

memsize = 32¶

merge()¶

impro.analysis.alpha_shape_gpu.get_k_simplices(points: numpy.ndarray)¶

Parameters:	points (np.array) – nx2 array of points to use for alpha complex
Returns:	alpha complex (mx5 array of d=1 simplices containing the upper and lower limits for a simplice to be interior/) on boundary of the alpha shape.

Filter¶

Author:	Sebastian Reinhard
Organization:	Biophysics and Biotechnology, Julius-Maximillians-University of Würzburg
Version:	2019.06.26

class impro.analysis.filter.Filter¶

Bases: object

static local_density_filter(points, r, n)¶

Get the indices of all points having a minimum of n neighbors in a radius of r

Parameters:	points (np.array) – Points to filter (X,Y,Z) r (float) – Search for neighbors in a radius of r n (int) – Required neighbors in radius r to pass the filter
Returns:	filt – indices of entries passing the filter
Return type:	np.array

static values_filter(value, minimum, maximum)¶

Get the indices of an array values with value > minimum and value < maximum

Parameters:	value (np.array) – Array with values to filter minimum (float) – minimum value to pass the filter maximum (float) – maximum value to pass the filter
Returns:	filt – indices of entries passing the filter
Return type:	np.array

Hough Transform¶

The General Hough Transform (GHT) maps the orientation of edge points in a template image to a predefined origin (typically the middle pixel of the image). Comparing this map with an image gives each point a rating of likelihood for being a source point of that map.

Author:	Sebastian Reinhard
Organization:	Biophysics and Biotechnology, Julius-Maximillians-University of Würzburg
Version:	2019.06.26

Example

>>> target = cv2.imread("path_to_file")
>>> template = cv2.imread("path_to_file")
>>> ght_target = GHTImage(target, blur=5, canny_lim=(130,180))
>>> H = HoughTransform()
>>> H.target = ght_target
>>> ght_template = TemplateImage(template)
>>> H.template = ght_template
>>> res = H.transform()

class impro.analysis.hough_transform_gpu.GHTImage(image, blur=4, canny_lim=(130, 200))¶

Bases: object

GHT specific image preprocessing

o_image¶

Input image

Type:	np.array

image¶

Resized and blurred input image

Type:	np.array

canny¶

Canny Edge processed image

Type:	np.array

gradient¶

Gradient image

Type:	np.array

class impro.analysis.hough_transform_gpu.HoughTransform(rotation_min=-10, rotation_max=10)¶

Bases: object

Perform Gradient Weighted General Hough Transform on the Graphics Processing Unit

rotation_min¶

Start matching template at rotation_min

Type:	float

rotation_max¶

End matching template at rotation_max

Type:	float

template¶

Matching template image on target image

Type:	np.array

target¶

Matching template image on target image

Type:	np.array

weighted¶

Weight the GHT by Gradient density

Type:	bool

transform()¶: Perform GHT algorithm with given data

rotation_max

rotation_min

target

template

transform()

class impro.analysis.hough_transform_gpu.Matrix(array)¶

Bases: object

Wrapper class for matrix and matrixf struct on GPU:

get()¶

class impro.analysis.hough_transform_gpu.TemplateImage(image, **kwargs)¶

Bases: impro.analysis.hough_transform_gpu.GHTImage

Extend GHTImage by templte properties

o_image¶

Input image

Type:	np.array

image¶

Resized and blurred input image

Type:	np.array

canny¶

Canny Edge processed image

Type:	np.array

gradient¶

Gradient image

Type:	np.array

r_matrix_zero¶

Vector mapping of edge points to a predefined origin

Type:	np.array

r_matrix¶

Rotated r_matrix_zero

Type:	np.array

rotate_r_matrix(angle)¶

Rotate R-Matrix by angle rad

angle: float: Angle to rotate matrix in rad

Analysis module¶

Analysis facade¶

Alpha Shape¶

Filter¶

Hough Transform¶

Module contents¶

Related Topics