大规模优化题目，Scipy？Ceres？PyTorch！

tsx81429  金牌会员 | 2024-7-18 22:34:29 | 显示全部楼层 | 阅读模式
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背景：
优化题目一般通过scipy.optimize或者Ceres Solver优化器求解。但在参数量较大的优化题目上，scipy提供的BFGS、L-BFGS-B、CG、SLSQP等梯度优化算法其复杂度和存储需求指数级上升，无法满足计算效率；而Ceres需要额外的语言来支持，当前算法工程师一般以python为主，学习本钱较大。且项目环境需要多语言混编，配置与摆设难度较大。
本文使用PyTorch/TensorFlow等呆板学习框架，通过主动求导高效计算梯度，避免手动计算梯度复杂性，使用CPU/CPU来加速求解优化题目。

PyTorch优化四部曲：
  1. # 优化迭代次数，设为1000次
  2. for _ in range(1000):
  3.     # 1. 清零梯度
  4.     optimizer.zero_grad()
  5.     # 通过调用 zero_grad()，我们清零了所有被优化参数的梯度。这是因为在 PyTorch 中，
  6.     # 每次进行反向传播时，梯度默认是累积的（即不会自动清零）。
  7.     # 如果不清理梯度，可能会导致累积误差，从而影响下一步的梯度计算。
  8.    
  9.     # 2. 计算损失函数
  10.     loss = objective_function(params)
  11.     # 这里我们计算当前参数下的目标函数值（损失函数）。
  12.     # 损失函数的值将作为后续反向传播计算梯度的基础。
  13.     # 根据参数（params）的当前值，求出损失值（即预测和实际的误差）。
  14.    
  15.     # 3. 反向传播计算梯度
  16.     loss.backward()
  17.     # 调用 loss.backward() 会进行反向传播，计算损失函数对所有优化参数的梯度。
  18.     # 这些梯度将存储在各个参数的 .grad 属性中，以便在优化步骤中使用。
  19.    
  20.     # 4. 更新参数
  21.     optimizer.step()
  22.     # 调用 optimizer.step() 会应用优化器来更新参数。
  23.     # 优化器会利用刚才计算的梯度（存储在 .grad 属性中），按照指定优化算法（如 Adam）
  24.     # 的规则更新参数。这样一来，参数会朝着能最小化损失函数的方向一步步调整。
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开胃小菜：
在三维空间中，给定初始点（0,0,0），求解优化使其距离点(2,3,4)近来。
  1. import torch
  3. # 定义目标函数，取任意数量优化变量
  4. def objective_function(params):
  5.     x, y, z = params
  6.     return (x - 2)**2 + (y - 3)**2 + (z - 4)**2
  8. # 初始化优化变量
  9. params = [torch.tensor([0.0], requires_grad=True),
  10.           torch.tensor([0.0], requires_grad=True),
  11.           torch.tensor([0.0], requires_grad=True)]
  13. # 优化器选择 Adam ，并传入列表参数
  14. optimizer = torch.optim.Adam(params, lr=0.1)
  16. # 迭代优化
  17. for _ in range(1000):
  18.     optimizer.zero_grad()
  19.     loss = objective_function(params)
  20.     loss.backward()
  21.     optimizer.step()
  23. # 输出优化结果
  24. print(f"Optimized x: {params[0].item()}")
  25. print(f"Optimized y: {params[1].item()}")
  26. print(f"Optimized z: {params[2].item()}")
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正餐：
假设场景：现有一张二维平面的游戏地图，并附带一份初始路网，请优化路网形状，使其平滑、美化、且与各个传送点保持挂接。
游戏地图如下，白色区域代表道路，黑色区域为地图外场景：

初始路网可视化见：

初始路网以link和node两张表表示：
node表
  1. {
  2. "type": "FeatureCollection",
  3. "crs": { "type": "name", "properties": { "name": "urn:ogc:def:crs:OGC:1.3:CRS84" } },
  4. "features": [
  5. { "type": "Feature", "properties": { "nodeid": "90cbaa72-3e8e-11ef-a98f-a13c99648c9a", "node_type": 1001.0 }, "geometry": { "type": "Point", "coordinates": [ 586.0, 795.0 ] } },
  6. { "type": "Feature", "properties": { "nodeid": "90cbaa9a-3e8e-11ef-a98f-a13c99648c9a", "node_type": null }, "geometry": { "type": "Point", "coordinates": [ 576.0, 788.0 ] } },
  7. { "type": "Feature", "properties": { "nodeid": "90cbaaf4-3e8e-11ef-a98f-a13c99648c9a", "node_type": null }, "geometry": { "type": "Point", "coordinates": [ 621.0, 780.0 ] } },
  8. { "type": "Feature", "properties": { "nodeid": "90cbaa18-3e8e-11ef-a98f-a13c99648c9a", "node_type": null }, "geometry": { "type": "Point", "coordinates": [ 592.0, 810.0 ] } },
  9. { "type": "Feature", "properties": { "nodeid": "90cba9f0-3e8e-11ef-a98f-a13c99648c9a", "node_type": null }, "geometry": { "type": "Point", "coordinates": [ 557.0, 822.0 ] } },
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  59. ]
  60. }
复制代码
link表
  1. {
  2. "type": "FeatureCollection",
  3. "crs": { "type": "name", "properties": { "name": "urn:ogc:def:crs:OGC:1.3:CRS84" } },
  4. "features": [
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  57. { "type": "Feature", "properties": { "linkid": "7cc693ca-3e8e-11ef-bae9-7993d366a9e1", "kind": "ske_solid", "snode_type": 1001.0, "enode_type": null, "snodeid": "90cbb620-3e8e-11ef-a98f-a13c99648c9a", "enodeid": "90cbb652-3e8e-11ef-a98f-a13c99648c9a" }, "geometry": { "type": "LineString", "coordinates": [ [ 1145.0, 385.0 ], [ 1138.0, 370.0 ] ] } },
  58. { "type": "Feature", "properties": { "linkid": "917f7e30-3e8e-11ef-a98f-a13c99648c9a", "kind": "ske_solid", "snode_type": 1001.0, "enode_type": null, "snodeid": "90cba996-3e8e-11ef-a98f-a13c99648c9a", "enodeid": "90cba72a-3e8e-11ef-a98f-a13c99648c9a" }, "geometry": { "type": "LineString", "coordinates": [ [ 581.0, 875.0 ], [ 569.0, 852.0 ], [ 546.0, 835.0 ] ] } },
  59. { "type": "Feature", "properties": { "linkid": "7cb7674c-3e8e-11ef-bae9-7993d366a9e1", "kind": "ske", "snode_type": null, "enode_type": null, "snodeid": "90cbb1a2-3e8e-11ef-a98f-a13c99648c9a", "enodeid": "90cbb3dc-3e8e-11ef-a98f-a13c99648c9a" }, "geometry": { "type": "LineString", "coordinates": [ [ 1101.0, 436.0 ], [ 1187.0, 556.0 ] ] } },
  60. { "type": "Feature", "properties": { "linkid": "918025ce-3e8e-11ef-a98f-a13c99648c9a", "kind": "ske", "snode_type": null, "enode_type": null, "snodeid": "90cbb3dc-3e8e-11ef-a98f-a13c99648c9a", "enodeid": "90cbb404-3e8e-11ef-a98f-a13c99648c9a" }, "geometry": { "type": "LineString", "coordinates": [ [ 1187.0, 556.0 ], [ 1290.0, 495.0 ], [ 1335.0, 549.0 ], [ 1333.0, 551.0 ] ] } },
  61. { "type": "Feature", "properties": { "linkid": "918089e2-3e8e-11ef-a98f-a13c99648c9a", "kind": "ske", "snode_type": null, "enode_type": null, "snodeid": "90cbb3dc-3e8e-11ef-a98f-a13c99648c9a", "enodeid": "90cbb0f8-3e8e-11ef-a98f-a13c99648c9a" }, "geometry": { "type": "LineString", "coordinates": [ [ 1187.0, 556.0 ], [ 1092.0, 623.0 ], [ 1078.0, 652.0 ], [ 1043.0, 654.0 ], [ 956.0, 708.0 ] ] } },
  62. { "type": "Feature", "properties": { "linkid": "91803c76-3e8e-11ef-a98f-a13c99648c9a", "kind": "ske", "snode_type": null, "enode_type": null, "snodeid": "90cbb04e-3e8e-11ef-a98f-a13c99648c9a", "enodeid": "90cbb0f8-3e8e-11ef-a98f-a13c99648c9a" }, "geometry": { "type": "LineString", "coordinates": [ [ 975.0, 767.0 ], [ 973.0, 761.0 ], [ 959.0, 754.0 ], [ 944.0, 722.0 ], [ 956.0, 708.0 ] ] } },
  63. { "type": "Feature", "properties": { "linkid": "7cb7a2b6-3e8e-11ef-bae9-7993d366a9e1", "kind": "ske", "snode_type": null, "enode_type": null, "snodeid": "90cbad1a-3e8e-11ef-a98f-a13c99648c9a", "enodeid": "90cbacf2-3e8e-11ef-a98f-a13c99648c9a" }, "geometry": { "type": "LineString", "coordinates": [ [ 862.0, 607.0 ], [ 785.0, 658.0 ], [ 769.0, 687.0 ] ] } },
  64. { "type": "Feature", "properties": { "linkid": "7cb7bada-3e8e-11ef-bae9-7993d366a9e1", "kind": "ske", "snode_type": null, "enode_type": null, "snodeid": "90cbacf2-3e8e-11ef-a98f-a13c99648c9a", "enodeid": "90cbac48-3e8e-11ef-a98f-a13c99648c9a" }, "geometry": { "type": "LineString", "coordinates": [ [ 769.0, 687.0 ], [ 801.0, 719.0 ], [ 861.0, 841.0 ] ] } }
  65. ]
  66. }
复制代码
  1. #自建link and node
  2. import numpy as np
  3. import cv2
  4. from skimage.morphology import skeletonize
  5. import torch
  6. import torch.optim as optim
  7. import torch.nn.functional as F
  8. import geopandas as gpd
  9. import shapely.geometry as G
  10. from scipy.interpolate import interp1d
  13. def read_binary_image(path):
  14.     """读取二值图像"""
  15.     img = cv2.imread(path, cv2.IMREAD_GRAYSCALE)
  16.     _, binary_img = cv2.threshold(img, 200, 255, cv2.THRESH_BINARY)
  17.     return binary_img
  19. #向量V单位化
  20. def normed(v):
  21.     return v/np.maximum(np.linalg.norm(v, axis=-1, keepdims=True), 1e-9)
  23. #插值
  24. def resample(xy, interval = 8.0, tol = 0.1):
  25.     xy = np.asarray(G.LineString(xy).simplify(tol, True).coords, np.double)
  26.     norms = np.linalg.norm(xy[1:] - xy[:-1], axis=1)
  27.     offs = np.empty(len(xy), xy.dtype)
  28.     offs[0] = 0
  29.     offs[1:] = np.add.accumulate(norms)
  30.     n = max(int(np.ceil(offs[-1]/interval)), 1)
  31.     kwargs = dict(copy=False, fill_value='extrapolate', assume_sorted=True)
  32.     xy = interp1d(offs, xy, axis=0, **kwargs)(
  33.       np.linspace(0, offs[-1], n + 1, dtype=xy.dtype))
  34.     return xy
  38. def generate_distance_transform(road_mask):
  39.     """生成距离变换图（反映每个像素到最近非路面像素的距离）;
  40.     为了保证修型后的线段不压盖边界，设计损失函数，当其里边界越近，损失越大；压盖边界时，损失极大"""
  41.     grid = cv2.distanceTransform(255 - road_mask, cv2.DIST_L2, 5)
  42.     # cv2.imwrite("grid.jpg",grid)
  44.     grid2 = cv2.distanceTransform(road_mask, cv2.DIST_L2, 5)
  45.     # cv2.imwrite("grid2.jpg",grid2)
  47.     grid = np.where(grid2 > 0, -grid2, grid)
  48.     grid = np.round(np.sqrt(np.tanh(grid/3) + 1)*45000).astype(np.int32)
  49.     # cv2.imwrite("tmp2.jpg",grid.astype(np.uint8))
  50.     # print(grid)
  51.     # print(np.max(grid),np.min(grid))
  52.     return grid
  54. def smooth_skeleton(nodes, links_dict, nodes_dict, dist_transform, fi, follow,lambda1=1.0, lambda2=1.0, lambda3=1.0, lambda4=1.0, lambda5=1.0, lambda6=1.0, max_iterations=50):
  55.     """使用 PyTorch 优化骨架节点，使骨架尽量平滑且不与非路面相交"""
  56.     device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
  57.     nodes_tensor = torch.tensor(nodes, dtype=torch.float32, requires_grad=True, device=device)
  58.     dist_transform_tensor = torch.tensor(dist_transform, dtype=torch.float32, device=device).unsqueeze(0).unsqueeze(0)
  59.     print(nodes_tensor.shape)
  60.     optimizer = optim.Adam([nodes_tensor], lr=0.03)
  61.     H, W = dist_transform.shape
  63.     #同一link相邻两个点
  64.     links_cons1 = []
  65.     for d in links_dict.values():
  66.         (b, e) = d['rng']
  67.         links_cons1.extend([(fi(i), fi(i + 1))
  68.                          for i in range(b, e - 1)])
  69.     links_cons1 = np.array(links_cons1)
  70.     initial_diffs = nodes[links_cons1[:, 0]] - nodes[links_cons1[:, 1]]
  71.     initial_distances = np.linalg.norm(initial_diffs, axis=1)
  72.     initial_distances = np.maximum(initial_distances, 1)
  74.     #同一link相邻三个点
  75.     links_cons2 = []
  76.     for d in links_dict.values():
  77.         (b, e) = d['rng']
  78.         if e-b <= 2:
  79.             continue
  80.         links_cons2.extend([(fi(i), fi(i + 1), fi(i + 2))
  81.                          for i in range(b, e - 2)])
  82.     links_cons2 = np.array(links_cons2)
  84.     #固定点
  85.     nods_cons1 = []
  86.     for d in links_dict.values():
  87.         mode = d["mode"]
  88.         (b, e) = d['rng']
  89.         if mode < 2 :
  90.             nods_cons1.append([fi(b)])
  91.     nods_cons1 = np.array(nods_cons1)
  92.     initial_solid = nodes[nods_cons1[:, 0]]  
  94.     #固定点射出方向
  95.     vecs_cons1 = []
  96.     for d in links_dict.values():
  97.         mode = d["mode"]
  98.         (b, e) = d['rng']
  99.         if mode == 1:
  100.             vecs_cons1.append([fi(b), fi(b+1)])
  101.     vecs_cons1 = np.array(vecs_cons1)
  102.     initial_vecs1 = nodes[vecs_cons1[:, 0]] - nodes[vecs_cons1[:, 1]]
  104.     #多link挂接时，角度均匀
  105.     vecs_cons2 = []
  106.     #多link挂接时，近似180度的两个射出角保持直线
  107.     vecs_cons3 = []
  108.     for d in nodes_dict.values():
  109.         node_couple_list = d["vecs"]
  110.         if len(node_couple_list) >= 2:
  111.             for idx in range(len(node_couple_list)):
  112.                 (s,e) = node_couple_list[idx]
  113.                 if len(node_couple_list) == idx+1:
  114.                     (ss,ee) = node_couple_list[0]
  115.                 else:
  116.                     (ss,ee) = node_couple_list[idx+1]
  117.                 vecs_cons2.append([fi(s), fi(e), fi(ss), fi(ee)])
  118.                 if abs(np.arctan2(np.cross(nodes[fi(s)] - nodes[fi(e)] , nodes[fi(ss)] - nodes[fi(ee)]), (nodes[fi(s)] - nodes[fi(e)] )@(nodes[fi(ss)] - nodes[fi(ee)])))>2.8:
  119.                     vecs_cons3.append([fi(e), fi(s), fi(ee)])
  120.     vecs_cons2 = np.array(vecs_cons2)
  121.     vecs_cons3 = np.array(vecs_cons3)
  122.     links_cons2 = np.concatenate([links_cons2,vecs_cons3],axis=0)
  124.    
  125.     for _ in range(max_iterations):
  126.         optimizer.zero_grad()
  128.         # 平滑项
  129.         # smoothness_term = torch.sum(torch.norm(nodes_tensor[links[:, 0]] - nodes_tensor[links[:, 1]], dim=1))
  130.         # 保持与初始距离的比例，且最小长度为1个像素
  131.         length__start_points = nodes_tensor[links_cons1[:, 0]]
  132.         length__end_points = nodes_tensor[links_cons1[:, 1]]
  133.         length__distances = torch.norm(length__start_points - length__end_points, dim=1)
  134.         smoothness_term = torch.sum((length__distances - torch.tensor(initial_distances, device=device))**2)  
  135.         
  136.         # 平滑项，角度均匀
  137.         first_points = nodes_tensor[links_cons2[:, 0]]
  138.         second_points = nodes_tensor[links_cons2[:, 1]]
  139.         third_points = nodes_tensor[links_cons2[:, 2]]
  140.         smoothness_term2 = (1 - F.cosine_similarity((second_points-first_points).unsqueeze(0), (third_points-second_points).unsqueeze(0), dim=1)).sum()
  141.         # print("debug",smoothness_term2)
  143.         #固定点
  144.         solid_points = nodes_tensor[nods_cons1[:, 0]]
  145.         solid_term = torch.sum(torch.norm(solid_points - torch.tensor(initial_solid, device=device), dim=1))
  147.         #固定射出角度
  148.         solid_first_points = nodes_tensor[vecs_cons1[:, 0]]
  149.         solid_second_points = nodes_tensor[vecs_cons1[:, 1]]
  150.         solid_vecs_term = (1 - F.cosine_similarity((solid_first_points-solid_second_points).unsqueeze(0), torch.tensor(initial_vecs1, device=device).unsqueeze(0), dim=1)).sum()
  152.         # 距离项
  153.         # 将节点坐标转换为插值中的标准化坐标并取样
  154.         grid = nodes_tensor.unsqueeze(0).unsqueeze(0)  # [1, 1, N, 2]
  155.         grid = torch.cat((grid[:, :, :, 0:1] * 2 / (W - 1) - 1, grid[:, :, :, 1:2] * 2 / (H - 1) - 1), dim=3)
  156.         sampled_dist = F.grid_sample(dist_transform_tensor, grid, mode='bilinear', padding_mode='border', align_corners=True)
  157.         distance_term = sampled_dist.view(-1).sum()
  159.         #多度点均匀挂接
  160.         one_vec = nodes_tensor[vecs_cons2[:, 0]] - nodes_tensor[vecs_cons2[:, 1]]
  161.         the_other_vec = nodes_tensor[vecs_cons2[:, 2]] - nodes_tensor[vecs_cons2[:, 3]]
  162.         # 计算点积
  163.         dot_products = torch.sum(one_vec * the_other_vec, dim=1)
  164.         cross_products = one_vec[:, 0] * the_other_vec[:, 1] - one_vec[:, 1] * the_other_vec[:, 0]
  165.         # 计算夹角
  166.         nodes_angles = torch.atan2(cross_products, dot_products)
  167.         # 将结果张量的形状调整为 (100, 1)
  168.         nodes_angles = nodes_angles.view(-1, 1)
  169.         nodes_vecs_term = torch.sum(torch.max(- nodes_angles + torch.full_like(nodes_angles, torch.tensor(torch.pi / 2)),torch.full_like(nodes_angles, torch.tensor(0))))
  171.         # #近似180度挂接的保持直线
  172.         # vecs_cons3
  173.         
  174.         
  175.         loss = (lambda1 * smoothness_term +  #保持原有长度损失
  176.                lambda2 * distance_term +  #grid损失
  177.                lambda3 * smoothness_term2 +  #角度平滑损失
  178.                lambda4 * solid_term +  #固定点不动约束
  179.                lambda5 * solid_vecs_term +#固定点射出角约束
  180.                lambda6 * nodes_vecs_term #多度挂接角度均匀
  181.                )
  182.         loss.backward()
  183.         
  184.         optimizer.step()
  185.         print(loss)
  187.     optimized_coords = nodes_tensor.cpu().detach().numpy()
  189.     for (i, j) in follow.items():
  190.         optimized_coords[i] = optimized_coords[j]
  191.     return optimized_coords
  193. def visualize_skeleton(binary_img, nodes, links, optimized_nodes,fi):
  194.     """可视化优化前后的骨架"""
  195.     img = cv2.cvtColor(binary_img, cv2.COLOR_GRAY2BGR)
  197.     view_links = []
  198.     for d in links.values():
  199.         (b, e) = d['rng']
  200.         view_links.extend([(fi(i), fi(i + 1))
  201.                          for i in range(b, e - 1)])
  202.     links = np.array(view_links)
  203.     # 绘制原始骨架（红色）
  204.     for x, y in nodes:
  205.         cv2.circle(img, (x, y), 2, (0, 0, 255), -1)
  206.     for i, j in links:
  207.         cv2.line(img, tuple(nodes[i]), tuple(nodes[j]), (0, 0, 255), 1)
  209.     # # 绘制优化后的骨架（蓝色）
  210.     # for x, y in optimized_nodes:
  211.     #     cv2.circle(img, (int(x), int(y)), 2, (255, 0, 0), -1)
  212.     # for i, j in links:
  213.     #     cv2.line(img, tuple(optimized_nodes[i].astype(int)), tuple(optimized_nodes[j].astype(int)), (255, 0, 0), 1)
  215.     cv2.imwrite("res0.jpg",img)
  217. def out_gpd(links_gpdf,nodes_gpdf,links,pts,nodes):
  218.     links_gpdf = links_gpdf.set_geometry([
  219.           G.LineString(pts[b:e]).simplify(0.5, True)
  220.           for (b, e) in [links[k]['rng'] for k in links_gpdf['linkid']]])
  221.     nodes_gpdf = nodes_gpdf.set_geometry([
  222.           G.Point(pts[nodes[k]['vecs'][0][0]])
  223.           for k in nodes_gpdf['nodeid']])
  224.     gpd.GeoDataFrame(links_gpdf).to_file('./link2_out.geojson')
  225.     gpd.GeoDataFrame(nodes_gpdf).to_file('./node2_out.geojson')
  226.     return
  228. def main():
  229.     """主函数"""
  230.     # 读取二值图像
  231.     binary_img = read_binary_image('./1.jpg')
  232.     link_path = "./link.geojson"
  233.     node_path = "./node.geojson"
  234.    
  235.     link_gpd = gpd.read_file(link_path)
  236.     node_gpd = gpd.read_file(node_path)
  237.    
  238.     # 提取节点和连边
  239.     # 初始化节点字典，保存节点及其连出的向量信息
  240.     nodes = {}
  241.     for r in node_gpd.itertuples():
  242.         fixed = (not np.isnan(r.node_type))
  243.         nodes[r.nodeid] = {'vecs': []}
  244.     # 初始化点集列表和线段字典
  245.     pts = []
  246.     e = 0 #记录pts的idx
  247.     links = {}
  248.    
  249.     for r in link_gpd.itertuples():
  250.         #按照固定点类别区分模式
  251.         mode = (0 if (r.snode_type in [250]) else
  252.                 1 if (r.snode_type in [1001, 1002, 1003]) else 2)
  253.         xy = np.array(r.geometry.coords, np.double)
  254.         if mode == 1:
  255.             if len(xy) == 2:
  256.                 #如果固定点挂接的link是两个形点，那么添加一个靠近重点的四等分点，组成三个形点的link。
  257.                 xy = np.array([xy[0], (xy[0] + xy[1]*3)/4, xy[1]])
  258.                 #在插值的时候保留第一个点
  259.             xy = np.concatenate([xy[:1], resample(xy[1:])])
  260.         else:
  261.             xy = resample(xy)
  262.         pts.append(xy)
  263.         b = e
  264.         e += len(xy)
  265.         #当前link对应的pts点序从b到e-1
  266.         links[r.linkid] = {'rng': (b, e), 'mode': mode}
  267.         nodes[r.snodeid]['vecs'].append((b + 0, b + 1))
  268.         nodes[r.enodeid]['vecs'].append((e - 1, e - 2))
  270.     #三维展开成二维，即将所有的line坐标平铺，取消line维度  
  271.     pts = np.concatenate(pts)
  272.     # 用于记录同一个点的信息，对于每个节点，如果它连出多条边，将这些边的起点合并成一个。
  273.     follow = {}
  274.     for n in nodes.values():
  275.         l = n['vecs']
  276.         if len(l) > 2:
  277.             #计算node节点连的所有边的角度,并按照顺/逆时针调整顺序
  278.             v = np.array([pts[i2] - pts[i1] for (i1, i2) in l]).T
  279.             l[:] = [l[i] for i in np.argsort(np.arctan2(v[1], v[0]))]
  280.         #follow 字典，代表同一个点
  281.         if len(l) > 1:
  282.             for (i, _) in l[1:]:
  283.                 follow[i] = l[0][0]
  284.     def fi(i):
  285.         return follow.get(i, i)
  286.     print(pts.shape)
  287.     print(links["7cba8b52-3e8e-11ef-bae9-7993d366a9e1"])
  288.    
  289.     # 生成距离变换图
  290.     dist_transform = generate_distance_transform(binary_img)
  293. # lambda1  #保持原有长度损失
  294. # lambda2  #grid损失
  295. # lambda3  #角度平滑损失
  296. # lambda4 #固定点不动约束
  297. # lambda5 #固定点射出角约束
  298. # lambda6  #多度挂接角度均匀
  299.    
  300.     # 优化整个骨架
  301.     optimized_nodes = smooth_skeleton(pts, links, nodes, dist_transform, fi, follow, lambda1=1, lambda2=0.01, lambda3 = 2000000, lambda4 = 10000000,lambda5 = 10000000,lambda6=1400000, max_iterations=5000)
  303.     # 可视化优化前后的骨架
  304.     visualize_skeleton(binary_img, pts.astype(np.int32), links, optimized_nodes,fi)
  306.     # out gpd
  307.     out_gpd(link_gpd,node_gpd,links,optimized_nodes,nodes)
  309. if __name__ == '__main__':
  310.     main()
复制代码
优化后的结果见（蓝色）


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