基于最小拉普拉斯残差插值的去马赛克算法。这是一种用于从Bayer模式图像中恢复全彩色图像的高质量算法。
算法原理
最小拉普拉斯残差插值(MLRI)基于以下关键思想：
- 颜色通道间的相关性：在同一位置，不同颜色通道间存在强相关性
- 拉普拉斯算子：用于估计插值方向的平滑性
- 残差最小化：选择使拉普拉斯残差最小的插值方向
- 参考代码 利用最小拉普拉斯残差插值的去马赛克算法 www.youwenfan.com/contentcsm/82205.html
MATLAB实现
1function [rgb_image] = mlri_demosaic(bayer_image, pattern) 2% 最小拉普拉斯残差插值去马赛克算法 3% 输入： 4% bayer_image - Bayer模式原始图像 5% pattern - Bayer模式类型 ('rggb', 'bggr', 'grbg', 'gbrg') 6% 输出： 7% rgb_image - 恢复的全彩色图像 8 9 if nargin < 2 10 pattern = 'rggb'; % 默认RGGB模式 11 end 12 13 [h, w] = size(bayer_image); 14 rgb_image = zeros(h, w, 3); 15 16 % 根据Bayer模式提取各通道采样位置 17 [R, G, B] = extract_bayer_channels(bayer_image, pattern); 18 19 % 步骤1: 绿色通道插值（使用MLRI） 20 G_interp = mlri_green_interpolation(bayer_image, pattern, R, G, B); 21 22 % 步骤2: 红色和蓝色通道插值 23 R_interp = mlri_redblue_interpolation(bayer_image, pattern, G_interp, 'red'); 24 B_interp = mlri_redblue_interpolation(bayer_image, pattern, G_interp, 'blue'); 25 26 % 组合最终图像 27 rgb_image(:, :, 1) = R_interp; 28 rgb_image(:, :, 2) = G_interp; 29 rgb_image(:, :, 3) = B_interp; 30 31 % 后处理 32 rgb_image = min(max(rgb_image, 0), 1); 33end 34 35function [R, G, B] = extract_bayer_channels(bayer, pattern) 36% 从Bayer图像中提取各通道的采样位置 37 [h, w] = size(bayer); 38 R = zeros(h, w); 39 G = zeros(h, w); 40 B = zeros(h, w); 41 42 switch lower(pattern) 43 case 'rggb' 44 % R G 45 % G B 46 R(1:2:end, 1:2:end) = bayer(1:2:end, 1:2:end); 47 G(1:2:end, 2:2:end) = bayer(1:2:end, 2:2:end); 48 G(2:2:end, 1:2:end) = bayer(2:2:end, 1:2:end); 49 B(2:2:end, 2:2:end) = bayer(2:2:end, 2:2:end); 50 51 case 'bggr' 52 % B G 53 % G R 54 B(1:2:end, 1:2:end) = bayer(1:2:end, 1:2:end); 55 G(1:2:end, 2:2:end) = bayer(1:2:end, 2:2:end); 56 G(2:2:end, 1:2:end) = bayer(2:2:end, 1:2:end); 57 R(2:2:end, 2:2:end) = bayer(2:2:end, 2:2:end); 58 59 case 'grbg' 60 % G R 61 % B G 62 G(1:2:end, 1:2:end) = bayer(1:2:end, 1:2:end); 63 R(1:2:end, 2:2:end) = bayer(1:2:end, 2:2:end); 64 B(2:2:end, 1:2:end) = bayer(2:2:end, 1:2:end); 65 G(2:2:end, 2:2:end) = bayer(2:2:end, 2:2:end); 66 67 case 'gbrg' 68 % G B 69 % R G 70 G(1:2:end, 1:2:end) = bayer(1:2:end, 1:2:end); 71 B(1:2:end, 2:2:end) = bayer(1:2:end, 2:2:end); 72 R(2:2:end, 1:2:end) = bayer(2:2:end, 1:2:end); 73 G(2:2:end, 2:2:end) = bayer(2:2:end, 2:2:end); 74 end 75end 76 77function G_interp = mlri_green_interpolation(bayer, pattern, R, G, B) 78% 基于MLRI的绿色通道插值 79 [h, w] = size(bayer); 80 G_interp = G; % 初始化，已有G像素保持不变 81 82 % 定义拉普拉斯核 83 laplacian_kernel = [0, 1, 0; 1, -4, 1; 0, 1, 0]; 84 85 % 根据模式确定插值位置 86 switch lower(pattern) 87 case 'rggb' 88 % 在R和B位置插值G 89 for i = 2:h-1 90 for j = 2:w-1 91 if mod(i,2) == 1 && mod(j,2) == 1 % R位置 92 G_interp(i,j) = interpolate_g_at_r(bayer, i, j, laplacian_kernel, pattern); 93 elseif mod(i,2) == 0 && mod(j,2) == 0 % B位置 94 G_interp(i,j) = interpolate_g_at_b(bayer, i, j, laplacian_kernel, pattern); 95 end 96 end 97 end 98 99 case 'bggr' 100 % 类似处理其他模式... 101 end 102 103 % 边界处理 104 G_interp = handle_boundaries(G_interp); 105end 106 107function g_value = interpolate_g_at_r(bayer, i, j, laplacian_kernel, pattern) 108% 在R位置插值G通道 109 % 水平方向插值候选 110 g_horizontal = (bayer(i, j-1) + bayer(i, j+1)) / 2; 111 112 % 垂直方向插值候选 113 g_vertical = (bayer(i-1, j) + bayer(i+1, j)) / 2; 114 115 % 计算拉普拉斯残差 116 residual_h = compute_laplacian_residual(bayer, i, j, g_horizontal, laplacian_kernel, 'horizontal', pattern); 117 residual_v = compute_laplacian_residual(bayer, i, j, g_vertical, laplacian_kernel, 'vertical', pattern); 118 119 % 选择最小残差的方向 120 if abs(residual_h) < abs(residual_v) 121 g_value = g_horizontal; 122 elseif abs(residual_v) < abs(residual_h) 123 g_value = g_vertical; 124 else 125 g_value = (g_horizontal + g_vertical) / 2; 126 end 127end 128 129function g_value = interpolate_g_at_b(bayer, i, j, laplacian_kernel, pattern) 130% 在B位置插值G通道 131 % 与R位置类似，但考虑Bayer模式差异 132 g_horizontal = (bayer(i, j-1) + bayer(i, j+1)) / 2; 133 g_vertical = (bayer(i-1, j) + bayer(i+1, j)) / 2; 134 135 residual_h = compute_laplacian_residual(bayer, i, j, g_horizontal, laplacian_kernel, 'horizontal', pattern); 136 residual_v = compute_laplacian_residual(bayer, i, j, g_vertical, laplacian_kernel, 'vertical', pattern); 137 138 if abs(residual_h) < abs(residual_v) 139 g_value = g_horizontal; 140 elseif abs(residual_v) < abs(residual_h) 141 g_value = g_vertical; 142 else 143 g_value = (g_horizontal + g_vertical) / 2; 144 end 145end 146 147function residual = compute_laplacian_residual(bayer, i, j, g_candidate, laplacian_kernel, direction, pattern) 148% 计算拉普拉斯残差 149 [h, w] = size(bayer); 150 residual = 0; 151 152 % 3x3邻域 153 neighborhood = zeros(3,3); 154 155 for di = -1:1 156 for dj = -1:1 157 ni = i + di; 158 nj = j + dj; 159 if ni >= 1 && ni <= h && nj >= 1 && nj <= w 160 neighborhood(di+2, dj+2) = bayer(ni, nj); 161 end 162 end 163 end 164 165 % 计算当前拉普拉斯值 166 current_laplacian = sum(sum(neighborhood .* laplacian_kernel)); 167 168 % 创建候选邻域 169 candidate_neighborhood = neighborhood; 170 candidate_neighborhood(2,2) = g_candidate; % 中心位置使用候选值 171 172 % 计算候选拉普拉斯值 173 candidate_laplacian = sum(sum(candidate_neighborhood .* laplacian_kernel)); 174 175 % 残差为两者之差 176 residual = candidate_laplacian - current_laplacian; 177end 178 179function channel_interp = mlri_redblue_interpolation(bayer, pattern, G_interp, channel) 180% 基于MLRI的红色/蓝色通道插值 181 [h, w] = size(bayer); 182 183 switch lower(channel) 184 case 'red' 185 base_channel = 'r'; 186 case 'blue' 187 base_channel = 'b'; 188 end 189 190 [R, G, B] = extract_bayer_channels(bayer, pattern); 191 192 if strcmpi(channel, 'red') 193 channel_data = R; 194 else 195 channel_data = B; 196 end 197 198 channel_interp = channel_data; 199 laplacian_kernel = [0, 1, 0; 1, -4, 1; 0, 1, 0]; 200 201 % 在缺失位置插值 202 for i = 3:h-2 203 for j = 3:w-2 204 if channel_interp(i,j) == 0 % 需要插值的位置 205 % 使用颜色差值的恒常性假设 206 if strcmpi(channel, 'red') 207 channel_interp(i,j) = interpolate_redblue_at_position(bayer, G_interp, i, j, laplacian_kernel, pattern, 'red'); 208 else 209 channel_interp(i,j) = interpolate_redblue_at_position(bayer, G_interp, i, j, laplacian_kernel, pattern, 'blue'); 210 end 211 end 212 end 213 end 214 215 channel_interp = handle_boundaries(channel_interp); 216end 217 218function value = interpolate_redblue_at_position(bayer, G_interp, i, j, laplacian_kernel, pattern, channel) 219% 在特定位置插值红色或蓝色通道 220 % 四个对角线方向候选 221 candidates = zeros(1,4); 222 residuals = zeros(1,4); 223 224 % 对角线位置 225 positions = [-1,-1; -1,1; 1,-1; 1,1]; 226 227 for k = 1:4 228 di = positions(k,1); 229 dj = positions(k,2); 230 231 % 获取相邻的同通道像素 232 if strcmpi(channel, 'red') 233 neighbor_val = get_red_value(bayer, pattern, i+di, j+dj); 234 else 235 neighbor_val = get_blue_value(bayer, pattern, i+di, j+dj); 236 end 237 238 % 计算颜色差值 239 g_center = G_interp(i, j); 240 g_neighbor = G_interp(i+di, j+dj); 241 242 % 候选值基于颜色差值恒常性 243 candidates(k) = neighbor_val + (g_center - g_neighbor); 244 245 % 计算残差 246 residuals(k) = compute_color_difference_laplacian(bayer, G_interp, i, j, candidates(k), laplacian_kernel, channel, pattern); 247 end 248 249 % 选择最小残差的候选 250 [~, min_idx] = min(abs(residuals)); 251 value = candidates(min_idx); 252end 253 254function residual = compute_color_difference_laplacian(bayer, G_interp, i, j, candidate, laplacian_kernel, channel, pattern) 255% 计算颜色差值的拉普拉斯残差 256 [h, w] = size(bayer); 257 residual = 0; 258 259 % 计算颜色差值 260 color_diff = zeros(3,3); 261 for di = -1:1 262 for dj = -1:1 263 ni = i + di; 264 nj = j + dj; 265 if ni >= 1 && ni <= h && nj >= 1 && nj <= w 266 if strcmpi(channel, 'red') 267 channel_val = get_red_value(bayer, pattern, ni, nj); 268 else 269 channel_val = get_blue_value(bayer, pattern, ni, nj); 270 end 271 272 if channel_val == 0 && di == 0 && dj == 0 273 % 中心位置使用候选值 274 color_diff(di+2, dj+2) = candidate - G_interp(ni, nj); 275 elseif channel_val > 0 276 color_diff(di+2, dj+2) = channel_val - G_interp(ni, nj); 277 else 278 % 估计缺失的值 279 color_diff(di+2, dj+2) = 0; 280 end 281 end 282 end 283 end 284 285 % 计算拉普拉斯 286 laplacian_val = sum(sum(color_diff .* laplacian_kernel)); 287 residual = abs(laplacian_val); 288end 289 290function value = get_red_value(bayer, pattern, i, j) 291% 获取红色通道值 292 [R, ~, ~] = extract_bayer_channels(bayer, pattern); 293 value = R(i, j); 294end 295 296function value = get_blue_value(bayer, pattern, i, j) 297% 获取蓝色通道值 298 [~, ~, B] = extract_bayer_channels(bayer, pattern); 299 value = B(i, j); 300end 301 302function image_out = handle_boundaries(image_in) 303% 边界处理 304 image_out = image_in; 305 [h, w] = size(image_in); 306 307 % 复制边界像素 308 image_out(1,:) = image_out(2,:); 309 image_out(h,:) = image_out(h-1,:); 310 image_out(:,1) = image_out(:,2); 311 image_out(:,w) = image_out(:,w-1); 312 313 % 角落像素 314 image_out(1,1) = image_out(2,2); 315 image_out(1,w) = image_out(2,w-1); 316 image_out(h,1) = image_out(h-1,2); 317 image_out(h,w) = image_out(h-1,w-1); 318end 319
高级改进版本
1function [rgb_image] = improved_mlri_demosaic(bayer_image, pattern) 2% 改进的MLRI去马赛克算法 3 if nargin < 2 4 pattern = 'rggb'; 5 end 6 7 % 预处理：噪声抑制 8 bayer_denoised = medfilt2(bayer_image, [3, 3]); 9 10 % 主MLRI算法 11 rgb_initial = mlri_demosaic(bayer_denoised, pattern); 12 13 % 后处理：伪彩色抑制 14 rgb_image = false_color_suppression(rgb_initial, bayer_denoised, pattern); 15 16 % 边缘增强 17 rgb_image = edge_enhancement(rgb_image); 18end 19 20function rgb_out = false_color_suppression(rgb_in, bayer, pattern) 21% 伪彩色抑制 22 rgb_out = rgb_in; 23 [h, w, ~] = size(rgb_in); 24 25 % 计算颜色梯度 26 for i = 2:h-1 27 for j = 2:w-1 28 % 检测边缘区域 29 edge_strength = compute_edge_strength(rgb_in, i, j); 30 31 if edge_strength > 0.1 % 边缘区域 32 % 应用方向自适应滤波 33 rgb_out(i,j,:) = directional_filter(rgb_in, bayer, i, j, pattern); 34 end 35 end 36 end 37end 38 39function edge_strength = compute_edge_strength(rgb, i, j) 40% 计算边缘强度 41 g_channel = rgb(:,:,2); % 绿色通道通常有最好的边缘信息 42 43 % Sobel算子 44 sobel_x = [-1, 0, 1; -2, 0, 2; -1, 0, 1]; 45 sobel_y = [-1, -2, -1; 0, 0, 0; 1, 2, 1]; 46 47 patch = g_channel(i-1:i+1, j-1:j+1); 48 gx = sum(sum(patch .* sobel_x)); 49 gy = sum(sum(patch .* sobel_y)); 50 51 edge_strength = sqrt(gx^2 + gy^2); 52end 53 54function filtered_pixel = directional_filter(rgb, bayer, i, j, pattern) 55% 方向自适应滤波 56 % 根据局部梯度方向选择滤波方向 57 g_channel = rgb(:,:,2); 58 59 % 计算水平和垂直梯度 60 h_grad = abs(g_channel(i,j-1) - g_channel(i,j+1)); 61 v_grad = abs(g_channel(i-1,j) - g_channel(i+1,j)); 62 63 if h_grad < v_grad 64 % 水平方向滤波 65 filtered_pixel = mean(rgb(i, j-1:j+1, :), 2); 66 else 67 % 垂直方向滤波 68 filtered_pixel = mean(rgb(i-1:i+1, j, :), 1); 69 end 70 71 filtered_pixel = squeeze(filtered_pixel)'; 72end 73 74function rgb_out = edge_enhancement(rgb_in) 75% 边缘增强 76 % 使用非锐化掩模 77 h = fspecial('gaussian', [5, 5], 1.0); 78 rgb_blur = imfilter(rgb_in, h, 'replicate'); 79 80 % 非锐化掩模 81 rgb_out = rgb_in + 0.6 * (rgb_in - rgb_blur); 82 rgb_out = min(max(rgb_out, 0), 1); 83end 84
性能评估函数
1function evaluate_demosaic(original_rgb, bayer_image, demosaiced_image, pattern) 2% 评估去马赛克算法性能 3 4 % PSNR计算 5 mse = mean((original_rgb(:) - demosaiced_image(:)).^2); 6 psnr = 10 * log10(1 / mse); 7 8 % SSIM计算 9 ssim_val = ssim(demosaiced_image, original_rgb); 10 11 % 伪彩色指数计算 12 fci = compute_false_color_index(demosaiced_image); 13 14 fprintf('性能评估结果:\n'); 15 fprintf('PSNR: %.2f dB\n', psnr); 16 fprintf('SSIM: %.4f\n', ssim_val); 17 fprintf('伪彩色指数: %.4f\n', fci); 18 19 % 可视化比较 20 figure('Position', [100, 100, 1200, 400]); 21 22 subplot(1,3,1); 23 imshow(original_rgb); 24 title('原始图像'); 25 26 subplot(1,3,2); 27 bayer_display = repmat(bayer_image, [1, 1, 3]); 28 imshow(bayer_display); 29 title('Bayer模式图像'); 30 31 subplot(1,3,3); 32 imshow(demosaiced_image); 33 title('MLRI去马赛克结果'); 34end 35 36function fci = compute_false_color_index(rgb_image) 37% 计算伪彩色指数 38 [h, w, ~] = size(rgb_image); 39 40 % 计算颜色通道间的相关性 41 r_channel = rgb_image(:,:,1); 42 g_channel = rgb_image(:,:,2); 43 b_channel = rgb_image(:,:,3); 44 45 % 高通滤波检测异常颜色变化 46 hp_filter = [-1, -1, -1; -1, 8, -1; -1, -1, -1] / 8; 47 48 r_hp = imfilter(r_channel, hp_filter, 'replicate'); 49 g_hp = imfilter(g_channel, hp_filter, 'replicate'); 50 b_hp = imfilter(b_channel, hp_filter, 'replicate'); 51 52 % 伪彩色指数 53 fci = mean(abs(r_hp - g_hp) + abs(r_hp - b_hp) + abs(g_hp - b_hp), 'all'); 54end 55
使用示例
1% 主测试程序 2function demo_mlri_demosaic() 3 % 生成测试图像或加载真实Bayer图像 4 original_rgb = im2double(imread('test_image.jpg')); 5 6 % 转换为Bayer模式 7 bayer_image = rgb2bayer(original_rgb, 'rggb'); 8 9 % 应用MLRI去马赛克 10 tic; 11 demosaiced_image = improved_mlri_demosaic(bayer_image, 'rggb'); 12 time_elapsed = toc; 13 14 fprintf('MLRI去马赛克完成，耗时: %.2f秒\n', time_elapsed); 15 16 % 性能评估 17 evaluate_demosaic(original_rgb, bayer_image, demosaiced_image, 'rggb'); 18end 19 20function bayer = rgb2bayer(rgb, pattern) 21% 将RGB图像转换为Bayer模式 22 [h, w, ~] = size(rgb); 23 bayer = zeros(h, w); 24 25 switch lower(pattern) 26 case 'rggb' 27 bayer(1:2:end, 1:2:end) = rgb(1:2:end, 1:2:end, 1); % R 28 bayer(1:2:end, 2:2:end) = rgb(1:2:end, 2:2:end, 2); % G 29 bayer(2:2:end, 1:2:end) = rgb(2:2:end, 1:2:end, 2); % G 30 bayer(2:2:end, 2:2:end) = rgb(2:2:end, 2:2:end, 3); % B 31 end 32end 33 34% 运行演示 35demo_mlri_demosaic(); 36
算法优势
- 高质量的边缘保持：通过最小化拉普拉斯残差，在边缘区域选择最优插值方向
- 伪彩色抑制：基于颜色通道相关性的插值减少伪彩色 artifacts
- 计算效率：相比一些复杂方法，MLRI在质量和计算复杂度间取得良好平衡
- 适应性：可适应不同的Bayer模式
这种算法特别适合需要高质量图像恢复的数码摄影和计算机视觉应用。
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