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## Copyright (C) 2024 David Legland
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function varargout = polygonSkeleton(poly, varargin)
%POLYGONSKELETON Skeletonization of a polygon with a dense distribution of vertices.
%
% [V, ADJ] = polygonSkeleton(POLY)
% POLY is given as a N-by-2 array of polygon vertex coordinates. The
% result is given a Nv-by-2 array of skeleton vertex coordinates, and an
% adjacency list, as a NV-by-1 cell array. Each cell contains indices of
% vertices adjacent to the vertex indexed by the cell.
%
% [V, ADJ, RAD] = polygonSkeleton(POLY)
% Also returns the radius of each vertex, corresponding to the distance
% between the vertex and the closest point of the original contour
% polygon.
%
% SKEL = polygonSkeleton(POLY)
% Concatenates the results in a struct SKEL with following fields:
% * vertices the Nv-by-2 array of skeleton vertex coordinates
% * adjList the adjacency list of each vertex, as a Nv-by-1 cell array.
% * radius the Nv-by-1 array of radius for each vertex
%
% Example
% % start from a binary shape
% img = imread('circles.png');
% img = imFillHoles(img);
% figure; imshow(img); hold on;
% % compute a smooth contour
% cntList = imContours(img);
% cnts = smoothPolygon(cntList{1}, 5);
% drawPolygon(cnts, 'g');
% % compute skeleton
% [vertices, adjList] = polygonSkeleton(poly);
% % convert adjacency list to an edge array
% edges = adjacencyListToEdges(adjList);
% % draw the skeleton graph
% drawGraphEdges(vertices, edges);
%
% See also
% graphs, adjacencyListToEdges
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2020-05-29, using Matlab 9.8.0.1323502 (R2020a)
% Copyright 2020-2023 INRAE - BIA Research Unit - BIBS Platform (Nantes)
%% Voronoi Diagram computation
% Compute Voronoi Diagram, using polygon vertices as germs.
[V, C] = voronoin(poly);
% compute number of elements of each array
nVertices = size(V, 1);
nCells = size(C, 1);
% Detection of the vertices located inside the contour
insideFlag = inpolygon(V(:,1), V(:,2), poly(:,1), poly(:,2));
innerVertices = V(insideFlag, :);
% indices of inner vertices
indsInside = find(insideFlag);
nInnerVertices = length(indsInside);
% compute map between voronoi vertex indices and skeleton vertex indices.
vertexIndexMap = zeros(nVertices, 1);
for iVertex = 1:length(indsInside)
vertexIndexMap(indsInside(iVertex)) = iVertex;
end
%% Compute the topology of the skeleton
%
% Compute the topology as a list of adjacent vertex indices for each vertex
% inside the polygon.
% Need to convert between voronoi indices and skeleton indices.
% allocate adjacncy list
adjList = cell(nInnerVertices, 1);
vertexGermInds = zeros(nInnerVertices, 1);
% iterate on voronoi cells to compute skeleton by linking adjacent vertices
% (avoiding first cell which is located at infinity by convention)
for iGerm = 2:nCells
% vertices of current cell
cellVertices = C{iGerm};
nCellVertices = length(cellVertices);
% iterate on vertices of current cell
for k = 1:nCellVertices
% index of current voronoi vertex
iVertex = cellVertices(k);
% process only vertices within the contour
if insideFlag(iVertex) == 0
continue;
end
% convert voronoi vertex index to skeleton vertex index
indV1 = vertexIndexMap(iVertex);
% update the reference germ associated to current skeleton vertex
vertexGermInds(indV1) = iGerm;
% compute indices of adjacent vertices (in cell)
iPrev = cellVertices(mod(k - 2, nCellVertices) + 1);
iNext = cellVertices(mod(k, nCellVertices) + 1);
% keep only the neighbors within the polygon
if insideFlag(iPrev) == 1
adjList{indV1} = [adjList{indV1} vertexIndexMap(iPrev)];
end
if insideFlag(iNext) == 1
adjList{indV1} = [adjList{indV1} vertexIndexMap(iNext)];
end
end
end
% cleanup to avoid duplicate indices
for iVertex = 1:nInnerVertices
adjList{iVertex} = unique(adjList{iVertex});
end
%% Compute radius list
% for each voronoi vertex inside the polygon, compute the distance to
% original polygon.
% Find indices of germs associated to each vertex.
% By construction, each vertex is the circumcenter of three germs.
radiusList = zeros(nInnerVertices, 1);
for iVertex = 1:nInnerVertices
radiusList(iVertex) = norm(poly(vertexGermInds(iVertex),:) - innerVertices(iVertex,:));
end
%% Format output
if nargout <= 1
% format output to a struct
varargout{1} = struct('vertices', {innerVertices}, 'adjList', {adjList}, 'radius', {radiusList});
elseif nargout == 2
varargout = {innerVertices, adjList};
elseif nargout == 3
varargout = {innerVertices, adjList, radiusList};
end
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