mfjet.calculator_mf_pixel module#

class mfjet.calculator_mf_pixel.MFPixelCalculator(bin_width=1.0, eps=1e-06, mode='center', diagonal_connected=False)#

Bases: object

Minkowski functional calculator for the persistent analysis with Steiner-type formula in Manhattan geometry. This module is for pixelerated binary image analysis. This module is using shapely, and faster than marching square algorithm.

Parameters:

bin_width (float, default 1.) – pixel width
eps (float, default 1e-6) – epsilon parameter for determining points on the closed boundary of given pixel. For a pixel [x0,x1) x [y0,y1), the tolerance of covering points on the closed boundary will be

(x-x0) >= -(bin_width) * (eps), (y-y0) >= -(bin_width) * (eps).
mode (str, default is “center”) – If mode is “center”, pixel’s center will be used as its representative coordinate. For example, the origin (0,0) will be covered by a pixel [-bin_width/2, bin_width/2)x[-bin_width/2, bin_width/2)

If mode is “corner”, pixel’s left bottom corner will be used as its representative coordinate. For example, the origin (0,0) will be covered by a pixel [0, bin_width)x[0, bin_width/2)
diagonal_connected (bool, default False:) – If true, diagonally connected pixels will be considered as a connected piece. This flag will affect only calculation of Euler characteristics.

calc_mfs(coords, r)#

Compute MFs given points dilated by a square with half-width r. This function automatically takes care of pixelation of coords and discretization of dialation scale. The dilation scale r will be discretized as follows:

r -> Ceil[r / (bin_width*0.5)] * (bin_width*0.5)

Parameters:

coords (array_like with shape (N_pt, 2))
r (float or array_like) – Specifies the half-width of a square in the Minkowski sum.

Returns:

array of Minkowski functionals given r. The last index k is labeling $k$-th Minkiwski functionals

k=0: Euler characteristic k=1: Boundary length k=2: Area

Return type:

np.array with shape (3,) or (r.shape, 3)

class mfjet.calculator_mf_pixel.MFPixelCalculatorMarchingSquare(bin_width=1.0, eps=1e-06, mode='center', diagonal_connected=False)#

Bases: object

Parameters:

bin_width (float, default 1.) – pixel width
eps (float, default 1e-6) – epsilon parameter for determining points on the closed boundary of given pixel. For a pixel [x0,x1) x [y0,y1), the tolerance of covering points on the closed boundary will be

(x-x0) >= -(bin_width) * (eps), (y-y0) >= -(bin_width) * (eps).
mode (str, default is “center”) – If mode is “center”, pixel’s center will be used as its representative coordinate. For example, the origin (0,0) will be covered by a pixel [-bin_width/2, bin_width/2)x[-bin_width/2, bin_width/2)

If mode is “corner”, pixel’s left bottom corner will be used as its representative coordinate. For example, the origin (0,0) will be covered by a pixel [0, bin_width)x[0, bin_width/2)
diagonal_connected (bool, default False:) – If true, diagonally connected pixels will be considered as a connected piece. This flag will affect only calculation of Euler characteristics.

calc_mfs(coords=None, r=None, img=None)#

r -> Ceil[r / (bin_width*0.5)] * (bin_width*0.5)

Parameters:

coords (array_like with shape (N_pt, 2))
r (float or array_like) – Specifies the half-width of a square in the Minkowski sum.

Returns:

array of Minkowski functionals given r. The last index k is labeling $k$-th Minkiwski functionals

k=0: Euler characteristic k=1: Boundary length k=2: Area

Return type:

np.array with shape (3,) or (r.shape, 3)

coord_to_img(coord)#

dilate_img_by_square(img, square_width)#

calc_mfs_from_img(img)#