更新grid算法beta

grid.py

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+import csv
+import numpy as np
+import matplotlib.pyplot as plt
+import math
+
+from shapely.geometry import box, MultiPoint
+from shapely.ops import unary_union
+from scipy.spatial import cKDTree
+from utils.gps_extractor import GPSExtractor
+
+
+# ---------------------- overlap 截断为不超过 10% ----------------------
+def clamp_overlap(overlap):
+    if overlap < 0:
+        return 0.0
+    elif overlap > 0.1:
+        return 0.1
+    else:
+        return overlap
+
+
+# ====================== 1) 生成可用矩形并记录其覆盖点集 ======================
+
+def generate_rectangles_with_point_indices(points, w, h, overlap=0.1, min_points=800):
+    """
+    在 bounding box 内，以 (w, h) + overlap 布置网格，生成所有矩形。
+    过滤：只保留"矩形内点数 >= min_points"的矩形。
+
+    返回:
+      rect_info_list: list of (rect_polygon, covered_indices)
+        - rect_polygon: Shapely Polygon
+        - covered_indices: 一个 set，表示该矩形覆盖的所有点索引
+    """
+    overlap = clamp_overlap(overlap)
+    if len(points) == 0:
+        return []
+
+    minx, miny = np.min(points, axis=0)
+    maxx, maxy = np.max(points, axis=0)
+
+    # 特殊情况：只有一个点或非常小范围 -> 很难满足 800 点
+    if abs(maxx - minx) < 1e-15 and abs(maxy - miny) < 1e-15:
+        return []
+
+    # 步长
+    step_x = w * (1 - overlap)
+    step_y = h * (1 - overlap)
+
+    x_coords = np.arange(minx, maxx + step_x, step_x)
+    y_coords = np.arange(miny, maxy + step_y, step_y)
+
+    # 建立 KDTree，加速查找
+    tree = cKDTree(points)
+    rect_info_list = []
+
+    for x in x_coords:
+        for y in y_coords:
+            rect_poly = box(x, y, x + w, y + h)
+            rx_min, ry_min, rx_max, ry_max = rect_poly.bounds
+
+            cx = (rx_min + rx_max) / 2
+            cy = (ry_min + ry_max) / 2
+            r = math.sqrt((rx_max - rx_min) ** 2 + (ry_max - ry_min) ** 2) / 2
+
+            candidate_ids = tree.query_ball_point([cx, cy], r)
+            if not candidate_ids:
+                continue
+
+            covered_set = set()
+            for idx_pt in candidate_ids:
+                px, py = points[idx_pt]
+                if rx_min <= px <= rx_max and ry_min <= py <= ry_max:
+                    covered_set.add(idx_pt)
+
+            # 如果覆盖的点数不足 min_points，就不保留
+            if len(covered_set) < min_points:
+                continue
+
+            rect_info_list.append((rect_poly, covered_set))
+
+    return rect_info_list
+
+
+# ====================== 2) 贪心算法选取子集覆盖所有点 ======================
+def cover_all_points_greedy(points, rect_info_list):
+    """
+    给定所有点 points 以及 "可用矩形+覆盖点集合" rect_info_list，
+    要求:
+       - 选出若干矩形，使得所有点都被覆盖 (每个点至少属于1个选中矩形)
+       - 最终并集面积最小 (做近似贪心)
+
+    返回:
+       chosen_rects: 最终选出的矩形列表 (每个是 shapely Polygon)
+    """
+
+    n = len(points)
+    all_indices = set(range(n))  # 所有点的索引
+    uncovered = set(all_indices)  # 尚未被覆盖的点索引
+
+    chosen_rects = []
+    union_polygon = None  # 当前已选矩形的并集
+
+    # 如果没有任何矩形可用，就直接失败
+    if not rect_info_list:
+        return []
+
+    # 为了在贪心过程中快速评估"新矩形带来的额外并集面积"，
+    # 我们每次选择矩形后更新 union_polygon，然后比较 union_polygon.union(new_rect).area - union_polygon.area
+    # 但 union_polygon 初始为 None
+
+    while uncovered:
+        best_gain = 0
+        best_new_area = float('inf')
+        best_rect = None
+        best_covered_new = set()
+
+        for rect_poly, covered_set in rect_info_list:
+            # 计算能覆盖多少"尚未覆盖"的点
+            newly_covered = uncovered.intersection(covered_set)
+            if not newly_covered:
+                continue
+
+            # 计算额外增加的并集面积
+            if union_polygon is None:
+                # 第一次选，union_polygon 为空 => new_area = rect_poly.area
+                new_area = rect_poly.area
+                area_increase = new_area
+            else:
+                # 计算 union_polygon ∪ rect_poly 的面积
+                test_union = union_polygon.union(rect_poly)
+                new_area = test_union.area
+                area_increase = new_area - union_polygon.area
+
+            # 贪心策略：最大化 (覆盖点数量) / (面积增量)
+            # 或者 equivalently, (覆盖点数量) 多、(面积增量) 小 都是好
+            ratio = len(newly_covered) / max(area_increase, 1e-12)
+
+            # 我们要找到 ratio 最大的那个
+            if ratio > best_gain:
+                best_gain = ratio
+                best_new_area = area_increase
+                best_rect = rect_poly
+                best_covered_new = newly_covered
+
+        if best_rect is None:
+            # 没有可选的矩形能覆盖任何剩余点 => 失败 (无法覆盖所有点)
+            return []
+
+        # 选中 best_rect
+        chosen_rects.append(best_rect)
+        uncovered -= best_covered_new
+
+        # 更新并集
+        if union_polygon is None:
+            union_polygon = best_rect
+        else:
+            union_polygon = union_polygon.union(best_rect)
+
+    return chosen_rects
+
+
+# ====================== 3) 主流程: 离散搜索 (w,h) + 贪心覆盖 ======================
+def find_optimal_rectangles_cover_all_points(
+        points,
+        base_w,
+        base_h,
+        overlap=0.1,
+        steps=5,
+        min_points=800
+):
+    """
+    在 [0.5*base_w,1.5*base_w] x [0.5*base_h,1.5*base_h] 的离散区间枚举 (w,h)，
+    - 生成可用矩形(≥800 点)的列表
+    - 用贪心算法选出子集来覆盖所有点
+    - 计算选中矩形的并集面积
+    选出面积最小的方案并返回
+    """
+    overlap = clamp_overlap(overlap)
+    n = len(points)
+    if n == 0:
+        return [], (base_w, base_h), 0.0  # 没有点就不用覆盖了
+
+    w_candidates = np.linspace(0.3 * base_w, 2 * base_w, steps)
+    h_candidates = np.linspace(0.3 * base_h, 2 * base_h, steps)
+
+    best_rects = []
+    best_area = float('inf')
+    best_w, best_h = base_w, base_h
+
+    for w in w_candidates:
+        for h in h_candidates:
+            rect_info_list = generate_rectangles_with_point_indices(points, w, h, overlap, min_points)
+            if not rect_info_list:
+                # 说明没有任何矩形能达到 "≥800点"
+                continue
+
+            # 用贪心覆盖所有点
+            chosen_rects = cover_all_points_greedy(points, rect_info_list)
+            if not chosen_rects:
+                # 无法覆盖所有点
+                continue
+
+            # 计算并集面积
+            union_poly = unary_union(chosen_rects)
+            area_covered = union_poly.area
+
+            if area_covered < best_area:
+                best_area = area_covered
+                best_rects = chosen_rects
+                best_w, best_h = w, h
+
+    return best_rects, (best_w, best_h), best_area
+
+
+# ====================== 4) 读取 CSV + 可视化 ======================
+def plot_image_points_cover_all_min_area(
+        image_dir,  # 新参数：图片文件夹路径
+        base_rect_width=0.001,
+        base_rect_height=0.001,
+        overlap=0.1,
+        steps=5,
+        min_points=800
+):
+    """
+    从图片文件夹读取GPS坐标:
+     1) 使用 GPSExtractor 从图片中提取GPS坐标
+     2) 在 [0.5*base_w,1.5*base_w] x [0.5*base_h,1.5*base_h] 离散搜索 (w,h)
+     3) 对每个 (w,h), 先生成所有"含≥800点"的矩形 => 再用贪心覆盖所有点 => 计算并集面积
+     4) 最小并集面积的方案即近似最优解
+     5) 最终用该方案可视化
+    """
+    overlap = clamp_overlap(overlap)
+
+    # 使用 GPSExtractor 读取图片GPS坐标
+    extractor = GPSExtractor(image_dir)
+    gps_df = extractor.extract_all_gps()
+    
+    if gps_df.empty:
+        print("未能从图片中提取到GPS坐标。")
+        return
+        
+    points = np.column_stack((gps_df['lon'], gps_df['lat']))  # (N, 2), [x=lon, y=lat]
+    n = len(points)
+    if n == 0:
+        print("No points extracted from images.")
+        return
+
+    # 贪心 + 离散搜索
+    chosen_rects, (best_w, best_h), best_area = find_optimal_rectangles_cover_all_points(
+        points,
+        base_w=base_rect_width,
+        base_h=base_rect_height,
+        overlap=overlap,
+        steps=steps,
+        min_points=min_points
+    )
+
+    if not chosen_rects:
+        print(f"无法找到满足 '每个矩形≥{min_points}点' 且覆盖所有点 的方案，试着调大尺寸/步数/overlap。")
+        return
+
+    # 可视化
+    plt.figure(figsize=(10, 8))
+    # 画点
+    plt.scatter(points[:, 0], points[:, 1], c='red', s=10, label='Points')
+
+    # 画矩形
+    for i, rect in enumerate(chosen_rects):
+        if rect.is_empty:
+            continue
+        x, y = rect.exterior.xy
+        plt.fill(x, y, edgecolor='green', fill=False, alpha=0.3,
+                 label='Chosen Rectangles' if i == 0 else "")
+
+    plt.title(
+        f"Cover All Points, Each Rect≥{min_points} pts, Minimal Union Area\n"
+        f"base=({base_rect_width:.6f} x {base_rect_height:.6f}), overlap≤{overlap}, steps={steps}\n"
+        f"best (w,h)=({best_w:.6f},{best_h:.6f}), union area={best_area:.6f}, #rect={len(chosen_rects)}"
+    )
+    plt.xlabel("Longitude")
+    plt.ylabel("Latitude")
+    plt.legend()
+    plt.grid(True)
+    plt.show()
+
+
+# ------------------ 测试入口 ------------------
+if __name__ == "__main__":
+    image_dir = r"C:\datasets\134\code\images"  # 替换为你的图片文件夹路径
+    plot_image_points_cover_all_min_area(
+        image_dir,
+        base_rect_width=0.01,
+        base_rect_height=0.01,
+        overlap=0.05,  # 会被截断到 0.1
+        steps=40,
+        min_points=100
+    )