Source code for cortex.polyutils.distortion


import numpy as np


[docs] class Distortion(object): """Used to compute distortion metrics between fiducial and another (e.g. flat) surface. Parameters ---------- flat : 2D ndarray, shape (total_verts, 3) Location of each vertex in flatmap space. ref : 2D ndarray, shape (total_verts, 3) Location of each vertex in fiducial (reference) space. polys : 2D ndarray, shape (total_polys, 3) Triangle vertex indices in both `flat` and `ref`. """
[docs] def __init__(self, flat, ref, polys): self.flat = flat self.ref = ref self.polys = polys
@property def areal(self): """Compute areal distortion of the flatmap. Areal distortion is calculated at each triangle as the log2 ratio of the triangle area in the flatmap to the area in the reference surface. Distortion values are then resampled onto the vertices. Thus a value of 0 indicates the areas are equal (no distortion), a value of +1 indicates that the area in the flatmap is 2x the area in the reference surface (expansion), and a value of -1 indicates that the area in the flatmap is 1/2x the area in the reference surface (compression). See: http://brainvis.wustl.edu/wiki/index.php/Caret:Operations/Morphing Returns ------- vertratios : 1D ndarray, shape (total_verts,) Areal distortion at each vertex. """ def area(pts, polys): ppts = pts[polys] cross = np.cross(ppts[:,1] - ppts[:,0], ppts[:,2] - ppts[:,0]) return np.sqrt((cross**2).sum(-1)) refarea = area(self.ref, self.polys) flatarea = area(self.flat, self.polys) tridists = np.log2(flatarea/refarea) vertratios = np.zeros((len(self.ref),)) vertratios[self.polys[:,0]] += tridists vertratios[self.polys[:,1]] += tridists vertratios[self.polys[:,2]] += tridists vertratios /= np.bincount(self.polys.ravel(), minlength=len(self.ref)) vertratios = np.nan_to_num(vertratios) vertratios[vertratios==0] = 1 return vertratios @property def metric(self): """Compute metric distortion of the flatmap. Metric distortion is calculated as the difference in squared distance from each vertex to its neighbors between the flatmap and the reference. Positive values of metric distortion mean that vertices are farther from their neighbors in the flatmap than in the reference surface (expansion), etc. See: Fishl, Sereno, and Dale, 1999. Returns ------- vertdists : 1D ndarray, shape (total_verts,) Metric distortion at each vertex. """ import networkx as nx def iter_surfedges(tris): for a,b,c in tris: yield a,b yield b,c yield a,c def make_surface_graph(tris): graph = nx.Graph() graph.add_edges_from(iter_surfedges(tris)) return graph G = make_surface_graph(self.polys) selverts = np.unique(self.polys.ravel()) ref_dists = [np.sqrt(((self.ref[np.array([x for x in G.neighbors(ii)])] - self.ref[ii])**2).sum(1)) for ii in selverts] flat_dists = [np.sqrt(((self.flat[np.array([x for x in G.neighbors(ii)])] - self.flat[ii])**2).sum(1)) for ii in selverts] msdists = np.array([(f-r).mean() for r,f in zip(ref_dists, flat_dists)]) alldists = np.zeros((len(self.ref),)) alldists[selverts] = msdists return alldists