From b8a8ff2bc662c89e102f22a3fefcd154b6bc32cd Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=88=98=E8=88=AA=E5=AE=87?= <3364451258@qq.com> Date: Wed, 6 May 2026 19:41:26 +0800 Subject: [PATCH] =?UTF-8?q?feat:=20cDNA=E5=BE=AE=E9=98=B5=E5=88=97?= =?UTF-8?q?=E5=9B=BE=E5=83=8F=E5=A4=84=E7=90=86=E4=BD=9C=E4=B8=9A=20-=20Py?= =?UTF-8?q?thon=E5=AE=9E=E7=8E=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 实现内容: - 网格划分:投影分析 + 自相关估周期 + 白顶帽去背景 + 质心提取 - 三种阈值分割:人工阈值、Otsu自动阈值、迭代阈值 - TV去噪(Chambolle投影算法) - 后处理:去小连通域 + 保留最大连通域 - 完整可视化:网格叠加、阈值对比、收敛曲线、分割结果 参考MATLAB代码:NewGridAndCV/demo_GriddingAndCV.m --- .gitignore | 14 + README.md | 118 +++ cDNA图像处理实例/图像处理实例.pptx | Bin 0 -> 1206403 bytes cDNA图像处理实例/数据/cDNA/Demo_cdna.m | 14 + cDNA图像处理实例/数据/cDNA/I_bw.jpg | Bin 0 -> 102533 bytes cDNA图像处理实例/数据/cDNA/cDNA.png | Bin 0 -> 103319 bytes results/result_I_bw.png | Bin 0 -> 5467 bytes results/result_full_segmentation.png | Bin 0 -> 275946 bytes results/result_gridding.png | 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a/.gitignore b/.gitignore new file mode 100644 index 0000000..aeb3680 --- /dev/null +++ b/.gitignore @@ -0,0 +1,14 @@ +# 大型数据文件(>10MB) +*.tif +*.TIF + +# MATLAB临时文件 +*.asv + +# Python +__pycache__/ +*.pyc + +# OS +.DS_Store +Thumbs.db diff --git a/README.md b/README.md new file mode 100644 index 0000000..574af15 --- /dev/null +++ b/README.md @@ -0,0 +1,118 @@ +# cDNA 微阵列图像处理作业资料 + +## 作业概述 + +本次作业涉及 **cDNA 微阵列(基因芯片)图像处理**,主要研究两个核心问题: + +1. **网格划分(Gridding)** - 定位微阵列图像中每个点的精确位置 +2. **图像分割(Segmentation)** - 区分前景(基因点)与背景 + +--- + +## 资料清单 + +### 1. 参考论文 + +| 文件名 | 作者 | 内容简介 | +|--------|------|----------| +| `2019-3-高污染基因芯片图像的网格划分_芦碧波.pdf` | 芦碧波 | 提出针对高污染基因芯片的网格划分方法,利用图像增强、分块处理和自动阈值检测来提高鲁棒性 | +| `封面+低对比度cDNA图像分割的局部水平集方法_芦碧波.pdf` | 芦碧波、刘利群、张霄宏、林忠华 | 提出基于局部信息的水平集方法,解决低对比度cDNA图像分割问题,引入局部图像拟合能量 | +| `显微图像分割.pdf` | - | 显微图像分割相关资料(密码保护,需另存为可读版本) | + +### 2. MATLAB 代码 + +#### `NewGridAndCV/` - 网格划分与C-V分割实现 + +| 文件名 | 功能说明 | +|--------|----------| +| `demo_GriddingAndCV.m` | **主程序** - 演示网格划分和Chan-Vese分割的完整流程 | +| `GriddingAndCV.m` | 网格划分核心算法,使用自相关估计点间距 | +| `cvseg.m` | Chan-Vese 水平集分割算法 | +| `chenvese.m` | C-V 模型的另一种实现 | +| `tvdenoise.m` | TV(Total Variation)去噪算法 | +| `choice.m` | 剔除面积过小的连通区域 | +| `choosemaxobj.m` | 保留最大连通区域 | +| `contour_bw.m` | 轮廓提取与二值化 | +| `fillingholes.m` | 填充孔洞 | +| `kappa.m` | 曲率计算 | +| `maskcircle2.m` | 圆形掩膜生成 | +| `redcolorcontour.m` | 红色轮廓显示 | +| `showphi.m` | 显示水平集函数 | + +#### `cDNA图像处理实例/` - 基础示例 + +| 文件名 | 功能说明 | +|--------|----------| +| `图像处理实例.pptx` | 实例讲解PPT | +| `数据/cDNA/Demo_cdna.m` | 基础演示代码 | +| `数据/cDNA/*.tif` | 测试图像数据 | + +### 3. 图像数据 + +| 文件名 | 说明 | +|--------|------| +| `GSM16390_CH1.tif` | 通道1原始图像(~26MB) | +| `GSM16390_CH2.tif` | 通道2原始图像(~26MB) | +| `GSM16390_CH2color.tif` | 彩色合成图像(~79MB) | +| `*_small.tif` | 上述图像的缩小版本 | +| `cDNA.png` | 测试用cDNA图像 | +| `I_bw.jpg` | 二值化结果示例 | +| `I_griddingout.tif` | 网格划分输出示例 | + +--- + +## 核心算法简介 + +### 网格划分算法流程 + +``` +1. 读取图像 → 转灰度 +2. 计算行/列投影(均值) +3. 自相关分析 → 估计点间距 +4. 形态学滤波 → 去除背景 +5. 阈值分割 → 标记峰值区域 +6. 提取质心 → 确定网格点位置 +``` + +### Chan-Vese 水平集分割 + +- **核心思想**:不依赖图像梯度,基于区域统计信息分割 +- **能量函数**:$E = \mu \cdot Length(C) + \nu \cdot Area(C) + \lambda_1 \int_{inside(C)} |I - c_1|^2 + \lambda_2 \int_{outside(C)} |I - c_2|^2$ +- **优势**:对模糊边缘和低对比度图像效果好 + +### 局部水平集方法(论文贡献) + +- 引入局部图像拟合能量 $E^{LIF}$ +- 使用高斯核 $K_\sigma$ 提取局部信息 +- 能有效处理灰度不均匀的cDNA图像 + +--- + +## 运行环境 + +- **MATLAB** R2016b 或更高版本 +- **需要工具箱**: + - Image Processing Toolbox + - Signal Processing Toolbox(用于自相关计算) + +--- + +## 快速开始 + +```matlab +% 1. 进入代码目录 +cd NewGridAndCV + +% 2. 运行演示 +demo_GriddingAndCV + +% 3. 或单独运行网格划分 +GriddingAndCV +``` + +--- + +## 参考文献 + +1. 芦碧波. 高污染基因芯片图像的网格划分[J]. 河南理工大学学报(自然科学版), 2019. +2. 芦碧波, 刘利群, 张霄宏, 林忠华. 低对比度cDNA图像分割的局部水平集方法[J]. 中国图象图形学报, 2014. diff --git a/cDNA图像处理实例/图像处理实例.pptx b/cDNA图像处理实例/图像处理实例.pptx new file mode 100644 index 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+参考MATLAB代码:NewGridAndCV/demo_GriddingAndCV.m, GriddingAndCV.m +""" + +import os +import numpy as np +import matplotlib.pyplot as plt +from matplotlib import rcParams +from PIL import Image +from scipy import ndimage +from skimage import filters, morphology, color + +# 中文字体设置 +rcParams['font.sans-serif'] = ['SimHei', 'Microsoft YaHei', 'DejaVu Sans'] +rcParams['axes.unicode_minus'] = False + +# 路径配置(使用脚本位置向上两级作为基准) +_SCRIPT_DIR = os.path.dirname(os.path.abspath(__file__)) +_BASE_DIR = os.path.dirname(_SCRIPT_DIR) # 项目根目录 +DATA_DIR = os.path.join(_BASE_DIR, 'cDNA图像处理实例', '数据', 'cDNA') +OUTPUT_DIR = os.path.join(_BASE_DIR, 'results') + + +# ============================================================ +# 第一部分:阈值分割算法 +# ============================================================ + +def manual_threshold(img_gray: np.ndarray, T: int) -> np.ndarray: + """人工固定阈值分割:灰度 > T 为前景""" + return (img_gray > T).astype(np.uint8) + + +def otsu_threshold(img_gray: np.ndarray) -> tuple[np.ndarray, float]: + """Otsu自动阈值分割:自动寻找最佳阈值""" + T = filters.threshold_otsu(img_gray) + binary = (img_gray > T).astype(np.uint8) + return binary, T + + +def iterative_threshold(img_gray: np.ndarray, tol: float = 1.0, max_iter: int = 100) -> tuple[np.ndarray, float, list]: + """ + 迭代阈值分割 + 算法流程: + 1. 初始阈值 T = 图像均值 + 2. 用T将像素分为前景和背景 + 3. 计算前景均值 μ_fg 和背景均值 μ_bg + 4. 更新 T_new = (μ_fg + μ_bg) / 2 + 5. 若 |T_new - T| < tol,停止;否则重复 + """ + T = float(np.mean(img_gray)) + history = [T] + for _ in range(max_iter): + fg = img_gray[img_gray > T] + bg = img_gray[img_gray <= T] + if len(fg) == 0 or len(bg) == 0: + break + T_new = (float(np.mean(fg)) + float(np.mean(bg))) / 2.0 + history.append(T_new) + if abs(T_new - T) < tol: + T = T_new + break + T = T_new + binary = (img_gray > T).astype(np.uint8) + return binary, T, history + + +# ============================================================ +# 第二部分:TV去噪(参考tvdenoise.m,Chambolle投影算法) +# ============================================================ + +def tv_denoise(f: np.ndarray, lam: float = 12.0, tol: float = 1e-2, max_iter: int = 200) -> np.ndarray: + """ + 全变分去噪 - Rudin-Osher-Fatemi模型 + min TV(u) + λ/2 ||f - u||² + 使用Chambolle投影算法求解 + """ + f = f.astype(np.float64) + dt = 0.25 + p1 = np.zeros_like(f) + p2 = np.zeros_like(f) + divp = np.zeros_like(f) + + for _ in range(max_iter): + lastdivp = divp.copy() + z = divp - f * lam + z1 = np.roll(z, -1, axis=1) - z + z2 = np.roll(z, -1, axis=0) - z + denom = 1.0 + dt * np.sqrt(z1**2 + z2**2) + p1 = (p1 + dt * z1) / denom + p2 = (p2 + dt * z2) / denom + divp = p1 - np.roll(p1, 1, axis=1) + p2 - np.roll(p2, 1, axis=0) + if np.max(np.abs(divp - lastdivp)) < tol: + break + + return f - divp / lam + + +# ============================================================ +# 第三部分:网格划分(参考GriddingAndCV.m) +# ============================================================ + +def estimate_spacing(profile: np.ndarray) -> int: + """ + 通过自相关分析估计点间距 + 参考MATLAB: ac = xcov(xProfile); maxima = find(s1>0 & s2<0); estPeriod = median(diff(maxima)) + """ + p = profile - np.mean(profile) + ac = np.correlate(p, p, mode='full') + ac = ac[len(p) - 1:] # 只取正半部分(lag >= 0) + + # 检测峰值:左斜率>0 且 右斜率<0(与MATLAB一致) + s1 = np.diff(ac, prepend=ac[0]) # 左斜率 + s2 = np.diff(ac, append=ac[-1]) # 右斜率 + maxima = np.where((s1 > 0) & (s2 < 0))[0] + + # 过滤掉lag=0附近的峰和过小的峰 + min_gap = len(profile) // 30 # 最小间距保护 + maxima = maxima[maxima > min_gap] + + if len(maxima) < 2: + return max(len(profile) // 16, 10) + + spacing = int(np.round(np.median(np.diff(maxima)))) + return max(spacing, 10) + + +def find_grid_centers(profile: np.ndarray, est_period: int) -> np.ndarray: + """ + 从投影曲线中提取网格中心位置 + 参考MATLAB流程: + imtophat(profile, strel('line', estPeriod, 0)) → 去背景 + graythresh → bwlabel → regionprops.Centroid → 提取质心 + """ + # 白顶帽变换:用长度为est_period的线性结构元素去除背景 + # MATLAB: seLine = strel('line', estPeriod, 0); xProfile2 = imtophat(xProfile, seLine) + # MATLAB中xProfile是1×N向量,这里用scipy的1D白顶帽实现 + profile_f = profile.astype(np.float64) + selem = np.ones(est_period) # 1D线性结构元素 + enhanced = ndimage.white_tophat(profile_f, structure=selem) + + # 自动阈值二值化(与MATLAB graythresh一致) + if enhanced.max() == 0: + return np.array([]) + T = filters.threshold_otsu(enhanced) + bw = (enhanced > T).astype(int) + + # 标记连通域并提取质心(与MATLAB bwlabel + regionprops一致) + labeled, num = ndimage.label(bw) + if num == 0: + return np.array([]) + + centers = [] + for i in range(1, num + 1): + indices = np.where(labeled == i)[0] + centers.append(float(np.mean(indices))) + return np.array(sorted(centers)) + + +def compute_grid_lines(centers: np.ndarray) -> np.ndarray: + """从中心点计算网格分割线(相邻中心的中点)""" + if len(centers) < 2: + return np.array([]) + gaps = np.diff(centers) / 2.0 + first = centers[0] - gaps[0] + last = centers[-1] + gaps[-1] + lines = [first] + for i in range(len(centers)): + if i < len(gaps): + lines.append(centers[i] + gaps[i]) + else: + lines.append(last) + return np.round(lines).astype(int) + + +def gridding(gray: np.ndarray) -> tuple: + """ + 完整网格划分流程 + 返回: x_grid, y_grid, col_profile, row_profile, x_period, y_period + """ + col_profile = np.mean(gray, axis=0).astype(np.float64) + row_profile = np.mean(gray, axis=1).astype(np.float64) + + x_period = estimate_spacing(col_profile) + y_period = estimate_spacing(row_profile) + + x_centers = find_grid_centers(col_profile, x_period) + y_centers = find_grid_centers(row_profile, y_period) + + x_grid = compute_grid_lines(x_centers) + y_grid = compute_grid_lines(y_centers) + + return x_grid, y_grid, col_profile, row_profile, x_period, y_period + + +# ============================================================ +# 第四部分:后处理(参考choice.m, choosemaxobj.m) +# ============================================================ + +def remove_small_objects(binary: np.ndarray, min_size: int = 20) -> np.ndarray: + """去除面积小于min_size的连通域""" + labeled, num = ndimage.label(binary) + result = binary.copy() + for i in range(1, num + 1): + if np.sum(labeled == i) < min_size: + result[labeled == i] = 0 + return result + + +def keep_largest_object(binary: np.ndarray, min_size: int = 20) -> np.ndarray: + """只保留最大连通域""" + labeled, num = ndimage.label(binary) + if num == 0: + return binary + areas = [int(np.sum(labeled == i)) for i in range(1, num + 1)] + max_area = max(areas) + if max_area < min_size: + return np.zeros_like(binary) + max_idx = int(np.argmax(areas)) + 1 + return (labeled == max_idx).astype(np.uint8) + + +# ============================================================ +# 第五部分:可视化 +# ============================================================ + +def plot_threshold_comparison(gray_block: np.ndarray, block_name: str = "子块") -> plt.Figure: + """对比三种阈值方法的分割结果""" + manual_T = int(np.mean(gray_block) * 0.6) + bw_manual = manual_threshold(gray_block, manual_T) + bw_otsu, T_otsu = otsu_threshold(gray_block) + bw_iter, T_iter, _ = iterative_threshold(gray_block) + + fig, axes = plt.subplots(2, 2, figsize=(10, 10)) + fig.suptitle(f'{block_name} - 三种阈值分割方法对比', fontsize=14) + + axes[0, 0].imshow(gray_block, cmap='gray') + axes[0, 0].set_title('原始灰度图') + axes[0, 0].axis('off') + + axes[0, 1].imshow(bw_manual, cmap='gray') + axes[0, 1].set_title(f'人工阈值 (T={manual_T})') + axes[0, 1].axis('off') + + axes[1, 0].imshow(bw_otsu, cmap='gray') + axes[1, 0].set_title(f'Otsu阈值 (T={T_otsu:.1f})') + axes[1, 0].axis('off') + + axes[1, 1].imshow(bw_iter, cmap='gray') + axes[1, 1].set_title(f'迭代阈值 (T={T_iter:.1f})') + axes[1, 1].axis('off') + + plt.tight_layout() + return fig + + +def plot_gridding_result(gray: np.ndarray, x_grid: np.ndarray, y_grid: np.ndarray, + col_profile: np.ndarray, row_profile: np.ndarray) -> plt.Figure: + """绘制网格划分结果""" + fig = plt.figure(figsize=(14, 10)) + fig.suptitle('cDNA微阵列网格划分结果', fontsize=14) + + ax1 = fig.add_subplot(2, 2, 1) + ax1.imshow(gray, cmap='gray') + for x in x_grid: + ax1.axvline(x=x, color='cyan', linewidth=0.5, alpha=0.7) + for y in y_grid: + ax1.axhline(y=y, color='cyan', linewidth=0.5, alpha=0.7) + ax1.set_title(f'网格叠加 ({len(x_grid)-1}列 x {len(y_grid)-1}行)') + ax1.axis('off') + + ax2 = fig.add_subplot(2, 2, 2) + ax2.plot(col_profile, 'b-', linewidth=0.5) + for x in x_grid: + ax2.axvline(x=x, color='r', linewidth=0.5, alpha=0.5) + ax2.set_title('列投影 (列均值)') + ax2.set_xlabel('列') + + ax3 = fig.add_subplot(2, 2, 3) + ax3.plot(row_profile, 'b-', linewidth=0.5) + for y in y_grid: + ax3.axvline(x=y, color='r', linewidth=0.5, alpha=0.5) + ax3.set_title('行投影 (行均值)') + ax3.set_xlabel('行') + + ax4 = fig.add_subplot(2, 2, 4) + ax4.hist(gray.ravel(), bins=50, color='gray', edgecolor='black', linewidth=0.3) + T_otsu = filters.threshold_otsu(gray) + ax4.axvline(x=T_otsu, color='r', linestyle='--', label=f'Otsu T={T_otsu:.0f}') + ax4.set_title('灰度直方图') + ax4.set_xlabel('灰度值') + ax4.legend() + + plt.tight_layout() + return fig + + +def plot_full_segmentation(gray: np.ndarray, bw_result: np.ndarray, title: str = "完整分割结果") -> plt.Figure: + """绘制完整分割结果""" + fig, axes = plt.subplots(1, 2, figsize=(12, 6)) + fig.suptitle(title, fontsize=14) + axes[0].imshow(gray, cmap='gray') + axes[0].set_title('原始灰度图') + axes[0].axis('off') + axes[1].imshow(bw_result, cmap='gray') + axes[1].set_title('二值分割结果') + axes[1].axis('off') + plt.tight_layout() + return fig + + +# ============================================================ +# 第六部分:主流程 +# ============================================================ + +def main() -> None: + os.makedirs(OUTPUT_DIR, exist_ok=True) + + # ---- 读取图像 ---- + img_path = os.path.join(DATA_DIR, 'cDNA.png') + print(f"读取图像: {img_path}") + img = np.array(Image.open(img_path)) + if img.ndim == 3: + gray = (color.rgb2gray(img[:, :, :3]) * 255).astype(np.uint8) + else: + gray = img + print(f"图像尺寸: {gray.shape}, 灰度范围: [{gray.min()}, {gray.max()}]") + + # ---- 步骤1: 网格划分 ---- + print("\n[步骤1] 网格划分...") + x_grid, y_grid, col_prof, row_prof, x_per, y_per = gridding(gray) + print(f" 列间距估计: {x_per}, 行间距估计: {y_per}") + print(f" 网格: {len(x_grid)-1} 列 x {len(y_grid)-1} 行") + + fig_grid = plot_gridding_result(gray, x_grid, y_grid, col_prof, row_prof) + fig_grid.savefig(os.path.join(OUTPUT_DIR, 'result_gridding.png'), dpi=150, bbox_inches='tight') + print(" 保存: result_gridding.png") + + # ---- 步骤2: 提取单个子块,三种阈值方法对比 ---- + print("\n[步骤2] 单块阈值分割对比...") + bi, bj = len(y_grid) // 2, len(x_grid) // 2 + if len(x_grid) >= 3 and len(y_grid) >= 3: + r1, r2 = y_grid[bi], y_grid[bi + 1] + c1, c2 = x_grid[bj], x_grid[bj + 1] + block = gray[r1:r2, c1:c2] + else: + h, w = gray.shape + bi, bj = 0, 0 + block = gray[h // 4:3 * h // 4, w // 4:3 * w // 4] + print(f" 选取子块 [{bi},{bj}]: 尺寸{block.shape}") + + fig_compare = plot_threshold_comparison(block, f"子块[{bi},{bj}]") + fig_compare.savefig(os.path.join(OUTPUT_DIR, 'result_threshold_compare.png'), dpi=150, bbox_inches='tight') + print(" 保存: result_threshold_compare.png") + + # 迭代阈值收敛过程 + _, T_iter, history = iterative_threshold(block) + fig_conv, ax_conv = plt.subplots(figsize=(6, 4)) + ax_conv.plot(history, 'bo-', markersize=3) + ax_conv.set_title('迭代阈值收敛过程') + ax_conv.set_xlabel('迭代次数') + ax_conv.set_ylabel('阈值T') + ax_conv.axhline(y=T_iter, color='r', linestyle='--', label=f'最终T={T_iter:.1f}') + ax_conv.legend() + fig_conv.savefig(os.path.join(OUTPUT_DIR, 'result_iterative_convergence.png'), dpi=100, bbox_inches='tight') + print(" 保存: result_iterative_convergence.png") + + # ---- 步骤3: 全图逐块分割(Otsu + TV去噪) ---- + print("\n[步骤3] 全图逐块分割...") + bw_full = np.zeros_like(gray) + if len(x_grid) >= 2 and len(y_grid) >= 2: + for i in range(len(y_grid) - 1): + for j in range(len(x_grid) - 1): + r1, r2 = y_grid[i], y_grid[i + 1] + c1, c2 = x_grid[j], x_grid[j + 1] + blk = gray[r1:r2, c1:c2].copy() + if blk.size == 0: + continue + # 暗图像增强(参考MATLAB: 均值<5则×5,<30则×1.5) + blk_mean = float(np.mean(blk)) + if blk_mean < 5: + blk = np.clip(blk.astype(float) * 5, 0, 255).astype(np.uint8) + elif blk_mean < 30: + blk = np.clip(blk.astype(float) * 1.5, 0, 255).astype(np.uint8) + # TV去噪 + blk_denoised = tv_denoise(blk.astype(float), lam=12.0) + # Otsu分割 + try: + T = filters.threshold_otsu(blk_denoised.astype(np.uint8)) + bw_blk = (blk_denoised > T).astype(np.uint8) + except ValueError: + bw_blk = np.zeros(blk.shape, dtype=np.uint8) + # 后处理:保留最大连通域 + bw_blk = keep_largest_object(bw_blk, min_size=8) + bw_full[r1:r2, c1:c2] = bw_blk + + bw_full = remove_small_objects(bw_full, min_size=20) + + fig_full = plot_full_segmentation(gray, bw_full, "全图逐块Otsu分割结果") + fig_full.savefig(os.path.join(OUTPUT_DIR, 'result_full_segmentation.png'), dpi=150, bbox_inches='tight') + print(" 保存: result_full_segmentation.png") + + bw_img = Image.fromarray((bw_full * 255).astype(np.uint8)) + bw_img.save(os.path.join(OUTPUT_DIR, 'result_I_bw.png')) + print(" 保存: result_I_bw.png") + + # ---- 步骤4: 网格叠加图 ---- + if img.ndim == 3: + overlay = img[:, :, :3].copy() + else: + overlay = np.stack([gray] * 3, axis=-1) + overlay = overlay.astype(np.uint8) + for x in x_grid: + if 0 <= x < overlay.shape[1]: + overlay[:, max(x - 1, 0):min(x + 2, overlay.shape[1]), :] = [0, 255, 255] + for y in y_grid: + if 0 <= y < overlay.shape[0]: + overlay[max(y - 1, 0):min(y + 2, overlay.shape[0]), :, :] = [0, 255, 255] + Image.fromarray(overlay).save(os.path.join(OUTPUT_DIR, 'result_gridding_overlay.png')) + print(" 保存: result_gridding_overlay.png") + + print(f"\n全部完成!输出文件在: {OUTPUT_DIR}") + + +if __name__ == '__main__': + main() diff --git a/参考资料/2019-3-高污染基因芯片图像的网格划分_芦碧波.pdf b/参考资料/2019-3-高污染基因芯片图像的网格划分_芦碧波.pdf new file mode 100644 index 0000000000000000000000000000000000000000..861e718c71a4f262531bc0ec72bdefdf2f7d73c7 GIT binary patch literal 2729392 zcmd41WmH|wmiJ5W;1FCl79hAg1Si4WosGLgaCZVhg9UeYcXxM!OK^9%n>;yB_vzF3 z?Y?)6GsgRYHP)( ztsLwD8Z4kjc>wF{Rf}H8&e}%M+6AD&0J2#*S?QPn94w4<8~`lO&~pHS?&%d>ZGZrJSv_MQfR7ImXl3{+h#lnl z7hxQ~hjPAN{|&+zU!PDO@INVIe0`#Sk;cgMdobhcg8o~?{k19oqqx^y`&V&)tvTcC zqW)XN{k1Xwqqx_d`xkLce=R%H?}PGh*jA>$cIJN)$MoN(0@Gj1&h+m}2B!aAHvI1P zXXQjec?wEbL3IXFCSe8u)9+0MfNaLU>_2<)m(2)Z`kgNS@Pp1c^Pgk>rvoE^`S;5I 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