Map (image) to Graph

Converting an input map (image) into a Graph

% THIS CODE IS DEVELOPED BY REZA JAVANMARD ALITAPPEH BY THE HELP OF KOSSAR
% JEDDISARAVI AND ADRIANO, WE ALSO USED A GRAPH LIBRARY FROM Carnegie Mellon University
%
% E-MAIL: [e-mail]
% 31/08/2018
%
% THE CODE GETS AN INPUT IMAGE AND CONVERTS INTO A GRAPH; THE NODES IN THIS
% GRAPH ARE MEETPOINTS AND ENDPOINT IN THE GVD
% AND THE OUTPUT IS TWO GRAPHS IN FORM OF: PIXEL PATH AND QUADRATIC CURVES
%
%------------------------------------------------------------------------------------
%
% PARAMETERS:
%
% INPUTS:---------------------------------------
% ** INPUT IMAGE: i.e. InputImage='Map8_2.jpg';
% THE INPUT IMAGE CAN BE .JPG OR .PNG OR .BMP ETC
%
% ** RADIUS: IT IS RADIUS OF THE ROBOT, THIS PARAMETER IS USED TO COMPUTE CONFIGURATION
% FREE SPACE, IN CASE IF THE GRAPH IS DISCONNECTED IT MEANS ROBOT'S RADIUS
% IS BIG AND IT CAN NOT PASS THROUGH A NARROW CORRIDOR OR DOOR IN THE
% MAP
%
% ** resolution: THIS PARAMETER IS USED TO CONVERT IMAGE SPACE INTO REAL
% SPAEC I.E. METER
%
% OUTPUTS:--------------------------------------
% ** GRAPH: CONTAINS NODES AND PATH BETWEEN NODES(IN PIXEL)
% path : n*2 matrix for x and y
% from : the corresponding start node
% to : the corresponding end node
%
% ** QUADGRAPH: CONTAINS THE GRAPH IN THE FORM OF QUADRATIC FUNCTION FOR
% EACH EDGE
% number_nodes: number of nodes in the constructed graph
% node_list: location of the nodes
% edge_matrix: Adjacency matrix of the graph
% path_matrix: The Path between all the nodes
% w_s : size of the work space
% Pol_coefs: coefficent of the quadratic form of the edges
% --------------------------------------------
% NOTES:
%
% * for the sake of clarity the function SHOWGRAPH shows how you can
% access tot the structures (GRAPH, QUADGRAPH)
% * If you work in other languages i.e Python, you can easily save the
% output in .Mat file and load it in Python.
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