提取动漫图像轮廓并拟合为样条曲线（MATLAB）

前言

之前有看到B站上的up主进行人工拟合，然后看到有评论说用MATLAB进行拟合的，就用deepseek生成了一下，只能说费时费力的感觉，一个是对于精度高的图像拟合效果特别差（大家可以用自己的证件照试一下），就比如用ai进行模糊照片的优化，他可以增加图片的像素点，但可能出现的结果不像自己；另一个只能识别轮廓，对于不同的图片还需要调试显示的阈值，之前就出现过把纯色背景也出现线条的，而用动漫图片进行处理，可能就是结果也不是很像。

而且对于生成的函数还不知道如何导入desmos，他虽然生成了一堆函数，但是我还不知道如何使用，自己试了十多分钟发现结果近似一条直线。

example | Desmoshttps://www.desmos.com/calculator/h2wsnoy3xi不知道是不是下面的这种方法，我是(x(t),y(t)),t的范围这样的形式，感觉不太对。

使用Python语言进行函数作画绘制芙莉莲&勇者-CSDN博客https://blog.csdn.net/weixin_64066303/article/details/148412637?spm=1001.2014.3001.5501使用Python进行函数作画-CSDN博客https://blog.csdn.net/weixin_64066303/article/details/148383559?spm=1001.2014.3001.5501形态学图像处理_形态学图像处理python-CSDN博客https://blog.csdn.net/weixin_64066303/article/details/138317780?ops_request_misc=%257B%2522request%255Fid%2522%253A%25229d7c4289359b3d8883f431656d0460a1%2522%252C%2522scm%2522%253A%252220140713.130102334.pc%255Fblog.%2522%257D&request_id=9d7c4289359b3d8883f431656d0460a1&biz_id=0&utm_medium=distribute.pc_search_result.none-task-blog-2~blog~first_rank_ecpm_v1~rank_v31_ecpm-2-138317780-null-null.nonecase&utm_term=%E8%BD%AE%E5%BB%93&spm=1018.2226.3001.4450Canny算子-CSDN博客https://blog.csdn.net/weixin_64066303/article/details/139259820?ops_request_misc=%257B%2522request%255Fid%2522%253A%2522128e956ccfd1321812df3ab3036e6f90%2522%252C%2522scm%2522%253A%252220140713.130102334.pc%255Fblog.%2522%257D&request_id=128e956ccfd1321812df3ab3036e6f90&biz_id=0&utm_medium=distribute.pc_search_result.none-task-blog-2~blog~first_rank_ecpm_v1~rank_v31_ecpm-1-139259820-null-null.nonecase&utm_term=%E7%AE%97%E5%AD%90&spm=1018.2226.3001.4450

代码

% 清除工作区和关闭所有图形窗口
clear; close all; clc;%% 1. 图像读取与高级预处理
imageName = 'example.png'; % 图片文件名
[~, name, ~] = fileparts(imageName); % 提取不带扩展名的文件名originalImg = imread(imageName);
figure; 
subplot(2,3,1); imshow(originalImg); title('原始图像');% 转换为灰度图
grayImg = rgb2gray(originalImg);% 增强图像对比度以提高边缘检测效果
grayImg = imadjust(grayImg);% 使用高斯滤波减少噪声
grayImg = imgaussfilt(grayImg, 1.5);% 使用多种方法结合进行二值化
% 方法1: Otsu's 方法
level_otsu = graythresh(grayImg);
bw_otsu = imbinarize(grayImg, level_otsu);% 方法2: 自适应阈值
bw_adaptive = imbinarize(grayImg, 'adaptive', 'Sensitivity', 0.5);% 结合两种方法
bwImg = bw_adaptive | bw_otsu;% 使用形态学操作清理图像
% 先去除小对象（噪声）
min_object_size = 100; % 增加最小对象大小
bwImg = bwareaopen(bwImg, min_object_size);% 填充小孔洞
bwImg = imfill(bwImg, 'holes');% 使用开运算平滑边缘
se = strel('disk', 3);
bwImg = imopen(bwImg, se);% 使用闭运算连接断开的边缘
se = strel('disk', 2);
bwImg = imclose(bwImg, se);subplot(2,3,2); imshow(bwImg); title('优化后的二值图像');%% 2. 高级边缘检测
% 使用多尺度边缘检测
edgeImg1 = edge(grayImg, 'canny', [0.05 0.2], 1.0); % 细边缘
edgeImg2 = edge(grayImg, 'canny', [0.1 0.3], 2.0);  % 粗边缘% 结合多尺度边缘
edgeImg = edgeImg1 | edgeImg2;% 使用Sobel算子增强边缘检测
sobelImg = edge(grayImg, 'sobel', 0.05);
edgeImg = edgeImg | sobelImg;% 清理边缘图像
edgeImg = bwareaopen(edgeImg, 20); % 去除小边缘
edgeImg = imdilate(edgeImg, strel('disk', 1)); % 稍微膨胀边缘subplot(2,3,3); imshow(edgeImg); title('多尺度边缘检测');% 结合二值图像和边缘图像
combinedEdges = edgeImg;
% 只保留在二值图像中存在的边缘区域
combinedEdges = combinedEdges & imdilate(bwImg, strel('disk', 5));subplot(2,3,4); imshow(combinedEdges); title('结合边缘');%% 3. 轮廓追踪
% 填充小孔洞，使轮廓更完整
filledEdges = imfill(combinedEdges, 'holes');% 使用bwboundaries追踪轮廓
B = bwboundaries(filledEdges, 'noholes');% 可视化轮廓
subplot(2,3,5); imshow(originalImg);
hold on;
for k = 1:length(B)boundary = B{k};% 只绘制足够长的轮廓if size(boundary, 1) > 50plot(boundary(:,2), boundary(:,1), 'r', 'LineWidth', 1); end
end
title('追踪到的轮廓');
hold off;%% 4. 智能关键点提取
simplifiedBoundaries = cell(size(B));
tolerance = 0.8; % 增加简化容差，减少关键点数量for k = 1:length(B)boundary = B{k};% 只处理足够长的轮廓if size(boundary, 1) < 50simplifiedBoundaries{k} = [];continue;end% 使用Ramer-Douglas-Peucker算法简化轮廓% 这里实现一个简化版本if size(boundary, 1) > 10% 计算轮廓总长度total_length = 0;for i = 2:size(boundary, 1)total_length = total_length + norm(boundary(i,:) - boundary(i-1,:));end% 根据轮廓长度动态调整简化程度dynamic_tolerance = tolerance * (total_length / 200);% 简化轮廓simplified = [boundary(1,:)];for i = 2:size(boundary, 1)-1if norm(boundary(i,:) - simplified(end,:)) > dynamic_tolerancesimplified = [simplified; boundary(i,:)];endendsimplified = [simplified; boundary(end,:)];simplifiedBoundaries{k} = simplified;elsesimplifiedBoundaries{k} = boundary;end
end%% 5. 高级曲线拟合
figure; 
imshow(ones(size(grayImg))); % 创建一个空白画布
hold on;
axis equal;
set(gca, 'YDir', 'reverse'); % 调整坐标方向，使其与图像坐标一致% 设置坐标轴范围与原始图像一致
axis([1 size(grayImg, 2) 1 size(grayImg, 1)]);% 存储所有拟合函数
splineFunctions = cell(length(simplifiedBoundaries), 1);for k = 1:length(simplifiedBoundaries)if isempty(simplifiedBoundaries{k})continue;endkeyPoints = simplifiedBoundaries{k};if size(keyPoints, 1) < 4 % 样条拟合至少需要4个点continue;end% 提取x和y坐标x = keyPoints(:, 2);y = keyPoints(:, 1);% 参数化样条拟合points = [x'; y'];splineCurve = cscvn(points);% 存储拟合函数splineFunctions{k} = splineCurve;% 绘制拟合后的曲线fnplt(splineCurve, 'b', 2);
end
title('用样条曲线拟合的动漫轮廓');
hold off;%% 6. 输出拟合函数信息并保存到文件
outputFileName = [name '.txt'];
fid = fopen(outputFileName, 'w');% 计算非空曲线数量
nonEmptyCount = sum(~cellfun(@isempty, splineFunctions));fprintf('共拟合了%d条曲线\n', nonEmptyCount);
fprintf(fid, '图像 "%s" 的轮廓拟合函数\n\n', imageName);
fprintf(fid, '共拟合了%d条曲线\n\n', nonEmptyCount);curveIdx = 1;
for i = 1:length(splineFunctions)if ~isempty(splineFunctions{i})fprintf('曲线%d: ', curveIdx);fprintf(fid, '曲线%d:\n', curveIdx);% 显示样条的基本信息breaks = splineFunctions{i}.breaks;pieces = splineFunctions{i}.pieces;order = splineFunctions{i}.order;dim = splineFunctions{i}.dim;coefs = splineFunctions{i}.coefs;fprintf('分段数: %d, 阶数: %d, 维度: %d\n', pieces, order, dim);fprintf(fid, '分段数: %d, 阶数: %d, 维度: %d\n', pieces, order, dim);% 检查coefs的维度[rows, cols] = size(coefs);% 修复系数矩阵维度问题if cols ~= piecesfprintf('警告: 系数矩阵的列数(%d)与分段数(%d)不匹配，尝试调整\n', cols, pieces);fprintf(fid, '警告: 系数矩阵的列数(%d)与分段数(%d)不匹配，尝试调整\n', cols, pieces);% 尝试修复：取较小的值作为实际分段数actual_pieces = min(cols, pieces);fprintf('使用实际分段数: %d\n', actual_pieces);fprintf(fid, '使用实际分段数: %d\n', actual_pieces);elseactual_pieces = pieces;end% 输出每段的函数表达式for j = 1:actual_pieces% 参数范围t_start = breaks(j);t_end = breaks(j+1);% 提取当前段的系数 - 修复索引问题if dim == 2% 二维样条：x和y分量% 确保索引不超出范围if order <= rowsx_coefs = coefs(1:order, j);if 2*order <= rowsy_coefs = coefs(order+1:2*order, j);elsefprintf('警告: 无法提取y系数，行数不足\n');fprintf(fid, '警告: 无法提取y系数，行数不足\n');continue;endelsefprintf('警告: 阶数(%d)大于系数矩阵行数(%d)\n', order, rows);fprintf(fid, '警告: 阶数(%d)大于系数矩阵行数(%d)\n', order, rows);continue;end% 构建x(t)和y(t)的多项式表达式x_expr = build_polynomial_expression(x_coefs, order, 't');y_expr = build_polynomial_expression(y_coefs, order, 't');fprintf('  段%d (t ∈ [%.2f, %.2f]):\n', j, t_start, t_end);fprintf('    x(t) = %s\n', x_expr);fprintf('    y(t) = %s\n', y_expr);fprintf(fid, '  段%d (t ∈ [%.2f, %.2f]):\n', j, t_start, t_end);fprintf(fid, '    x(t) = %s\n', x_expr);fprintf(fid, '    y(t) = %s\n', y_expr);elsefprintf('  非二维曲线，无法处理\n');fprintf(fid, '  非二维曲线，无法处理\n');endendfprintf('\n');fprintf(fid, '\n');curveIdx = curveIdx + 1;end
endfclose(fid);
fprintf('拟合函数已保存到文件: %s\n', outputFileName);%% 7. 将拟合结果与原始图像对比
figure;
subplot(1,2,1); imshow(originalImg); title('原始图像');subplot(1,2,2); 
% 创建与原始图像相同大小的白色背景
whiteBg = ones(size(grayImg));
imshow(whiteBg);
hold on;
axis equal;
set(gca, 'YDir', 'reverse');% 设置坐标轴范围与原始图像一致
axis([1 size(grayImg, 2) 1 size(grayImg, 1)]);for i = 1:length(splineFunctions)if ~isempty(splineFunctions{i})fnplt(splineFunctions{i}, 'b', 2);end
end
title('拟合结果');
hold off;%% 辅助函数：构建多项式表达式
function expr = build_polynomial_expression(coefs, order, var_name)expr = '';for k = 1:orderpower = order - k;coef = coefs(k);if abs(coef) > 1e-10 % 忽略非常小的系数if ~isempty(expr) && coef > 0expr = [expr ' + '];elseif ~isempty(expr) && coef < 0expr = [expr ' - '];coef = -coef;elseif isempty(expr) && coef < 0expr = [expr '-'];coef = -coef;endif power == 0expr = [expr num2str(coef, '%.6f')];elseif power == 1if abs(coef - 1) < 1e-10expr = [expr var_name];elseexpr = [expr num2str(coef, '%.6f') '*' var_name];endelseif abs(coef - 1) < 1e-10expr = [expr var_name '^' num2str(power)];elseexpr = [expr num2str(coef, '%.6f') '*' var_name '^' num2str(power)];endendendendif isempty(expr)expr = '0';end
end