v3.0.0
Shape analysis and classification routines for Mathematica
Copyright © 1997-2022 Flip Phillips, CC BY-NC 4.0.
See CHANGELOG.md for details.
A package for computing differential geometry using Mathematica.
Based on a bunch of work I've done since about 1995 or so. Bits and pieces borrowed from Koenderink, Gray, &c.
Right now, Shape is broken into five sub-modules:
- MapShape
- RegionShape
- ShapeMetrics
- ShapePatches
- Structure
Contains routines for calculating depth-map based shape using structure tensor shenanigans. All sigma default to 1.0 pixels.
imagePartials[img,sigma] returns {dix,diy,dixx,diyy,dixy} using a filter size of sigma.
structureTensor[img,sigma] computes an image containing the structure tensor with {J11,J22,J12} in {R,G,B}
orientationMap[img,sigma] returns an xyz orientation map in {R,G,B}.
ridgeMap[img,sigma] computes a ridge filter on img using a filter size of sigma.
tJunctionMap[img,sigma] computes a t-junction filter on img using a filter size of sigma.
vectorFieldMap[img,sigma] computes vector flow field on img using a filter size of sigma.
imagePartials[img,sigma] returns {dix,diy,dixx,diyy,dixy} on img using a filter size of sigma.
normalMap[img,sigma] gives an RGB normal map from img using a filter size of sigma.
flowMap[img,sigma] gives a flow direction map from img using a filter size of sigma.
formsMap[img,sigma] returns {e,f,g,E,F,G} map from img using filter size sigma.
curvaturesMap[img,sigma]returns a 2-channel kmin, kmax map from img using filter size sigma.
mapToImage[map,mask] turns a map into an image with optional mask.
A whole barrel of shape reparameterizations of
ToPrincipalCurvatures[H,K] gives kappa1 and kappa2 from mean and Gaussian curvatures. k1 <= k2
MeanCurvatureFromGradients[dx,dy,dxx,dyy,dxy] gives H from 1st and 2nd derivatives.
GaussianCurvatureFromGradientsComputes[dx,dy,dxx,dyy,dxy] K from 1st and 2nd derivatives.
GaussianCurvature[k1,k2] Gaussian curvature from principal curvatures k1,k2. Positive are synclastic, negative are anticlastic.
MeanCurvature[k1,k2] Mean curvature of k1,k2.
ShapeIndex[k1,k2] Koenderink's Shape Index.
Curvedness[k1,k2] Koenderink's Curvedness.
CurvatureContrast[k1,k2] Phillips/Perotti's contrast measure.
MichelsonContrast[k1,k2] Michaelson contrast measure.
NormalizedCurvatureContrast[k1,k2] Normalized Phillips/Perotti contrast measure.
TotalCurvature[k1,k2] Absolute total curvature.
MaximumCurvature[k1,k2] Absolute maximum curvature.
MaximumSignedCurvature[k1,k2] Absolute maximum curvature with sign.
ShapeIndexColor[si] Color coding on [-1,1] ala Koenderink. Green to red.
ShapeIndexCategory[si] Category coding on [-1,1] ala Koenderink. 1-9.
Generate simple parameterized shapes constrained by curvatures.
curvaturesPatch[u,v,k1,k2] is a parametric Monge-form patch from curvatures.
shapeCurvednessPatch[u,v,s,c] creates a parametric Monge-form patch from Shape Index and Curvedness.
meanGaussPatch[u,v,h,k] creates a parametric Monge-form patch from mean and Gaussian curvatures.
A start at stuff that derives structural information for objects. They make some assumptions about the representation. This is slowly being migrated from the 1.x Shape stuff.
VertexFrame[v,n,neighborhood] calculates the vertex frame for vertex v with normal n and neighbors.
OBJStructure[filename] calculates the differential structure of the OBJ file. This file should have vertex normals.
Will contain methods for applying shape calculations to Region