【路径规划】使用数学形态求解迷宫 - 找到穿过迷宫的路线（Matlab实现）

荧光Matlab

已于 2024-06-24 17:20:34 修改

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文章标签： matlab 开发语言

于 2024-06-24 16:54:59 首次发布

本文链接：https://blog.youkuaiyun.com/Matlab88888/article/details/139930951

“在代码的海洋里，有无尽的知识等待你去发现。我就是那艘领航的船，带你乘风破浪，驶向代码的彼岸。

💥💥💞💞欢迎来到本博客❤️❤️💥💥

🏆博主优势：🌞🌞🌞博客内容尽量做到思维缜密，逻辑清晰，为了方便读者。

⛳️座右铭：行百里者，半于九十。

📋📋📋本文目录如下：🎁🎁🎁

💥1 概述

本研究致力于利用数学形态学的方法来解决迷宫求解问题，旨在找出穿越迷宫的有效路线。迷宫作为一种复杂的拓扑结构，其路径寻找具有一定的难度和挑战性。数学形态学作为一种强大的数学工具，通过对迷宫的结构和特征进行分析和处理。研究中，可能会将迷宫转化为特定的数学模型，运用数学形态学的操作和算法，如膨胀、腐蚀、开运算、闭运算等，对迷宫的空间结构进行变换和推理。通过一系列的数学计算和逻辑判断，逐步探索迷宫中的可行路径，并筛选出最优的穿越路线。这种方法旨在提供一种高效、准确且具有普遍适用性的迷宫求解策略，为相关领域如人工智能、路径规划等提供有价值的理论和实践参考。

📚2 运行结果

部分代码：

function maze_solution
% Demo to solve a maze using mathematical morphology.
% This demo works for "perfect mazes."  A perfect maze is defined 
% as a maze which has one and only one path from any point in the 
% maze to any other point. This means that the maze has no
% inaccessible sections, no circular paths, and no open areas. 
% A perfect maze should have only 2 walls (I believe).
% No searching or optimization methods (such as A* or dynamic
% programming) are used - only morphology and standard image
% processing methods.
% Only tested for 8 bit integer color and monochrome images.
% Maze images should have dark walls on a light background.
% Maze may be surrounded by white, or go right out to the edge
% of the image and have the outer wall be the 
% outer boundary of the image.
% Clean up.
clc; 
close all; 
clear all; 
fontSize = 20;  % Font size for image captions.

% Change the current folder to the folder of this m-file.
% (The line of code below is from Brett Shoelson of The Mathworks.)
if(~isdeployed)
	cd(fileparts(which(mfilename)));
end
	
% For convenience in browsing, set a starting folder from which to browse.
startingFolder = 'C:\Documents and Settings\tk2013\My Documents\My Pictures\MISC\Mazes';
if ~exist(startingFolder, 'dir')
	% If that folder doesn't exist, just start in the current folder.
	startingFolder = pwd;
end

continueWithAnother = true;
promptMessage = sprintf('Please specify a maze image (in the next window).\nThis program will attempt to solve the maze.');
button = questdlg(promptMessage, 'maze_solution', 'OK', 'Cancel', 'OK');
if strcmpi(button, 'Cancel')
	continueWithAnother = false;
end

while continueWithAnother
	% Get the name of the maze image file that the user wants to use.
	defaultFileName = fullfile(startingFolder, '*.*');
	[baseFileName, folder] = uigetfile(defaultFileName, 'Select maze image file');
	if baseFileName == 0
		% User hit cancel.  Bail out.
		return;
	end
	fullFileName = fullfile(folder, baseFileName);


	% Here are some hard coded file names for ease in developing and debugging,
	% so we don't have to use uigetfile() all the time.

	% Gotten from http://www.erclc.org/StaffPages/David/Mazes/Maze1.gif
	% This maze works fine.
	% fullFileName = fullfile(folder, 'Maze1.gif');

	% Gotten from http://www.mattneuman.com/maze.htm
	% This is a test maze that won't work because it is not a "non-perfect maze."
	% fullFileName = fullfile(folder, 'Maze of Sisyphus.gif');

	% Open the maze image file.
	originalImage = imread(fullFileName);
	[rows cols numberOfColorBands] = size(originalImage);