import numpy as np import SimpleITK as sitk from scipy.ndimage import center_of_mass, rotate import matplotlib.pyplot as plt def _best_vertical_split(mask2d): """ binary 2D 陣列(最後一軸 = x):找讓 mask 與其鏡射重疊最大的垂直線 x = t。 c[s] = Σ_u A[u]·A[s-u] 是每列自卷積;批次 FFT 一次算出所有 s。 回傳 (score, s_best);s = 2·t(t 可能為半整數)。 """ n = mask2d.shape[-1] flat = np.asarray(mask2d).reshape(-1, n) rows = flat[flat.max(axis=1) > 0] if rows.size == 0: return 0.0, 0 L = 1 << (2 * n - 1).bit_length() padded = np.zeros((rows.shape[0], L), dtype=np.float32) padded[:, :n] = rows.astype(np.float32) F = np.fft.rfft(padded, axis=1) conv = np.fft.irfft(F * F, axis=1)[:, :2 * n - 1] score = np.clip(conv.sum(axis=0), 0, None) s_best = int(np.argmax(score)) return float(score[s_best]), s_best def best_symmetry_axis_angle(proj, coarse_step=10.0, fine_step=1.0): """ 2D binary 投影(axis0=row y, axis1=col x)的左右鏡稱軸搜尋: 將影像旋轉 θ 後,鏡稱軸變成垂直線(col = const),用 _best_vertical_split 評分; 粗搜 0..180°(coarse_step)再在 winner 附近細搜(fine_step)。 回傳 (theta_deg, score, s_best)。 """ base = (np.asarray(proj) > 0).astype(np.float32) best_th, best, best_s = 0.0, -1.0, 0 for th in np.arange(0.0, 180.0, coarse_step): sc, s = _best_vertical_split(rotate(base, th, reshape=False, order=0) > 0.5) if sc > best: best_th, best, best_s = float(th), sc, s for th in np.arange(best_th - coarse_step, best_th + coarse_step, fine_step): th2 = float(th) % 180.0 sc, s = _best_vertical_split(rotate(base, th2, reshape=False, order=0) > 0.5) if sc > best: best_th, best, best_s = th2, sc, s return best_th, best, best_s def _mirror_hit_count(X, Y, Z, n, d, m, sz, sy, sx): """每個骨 voxel 對平面 n·p=d 鏡射後四捨五入到最近 voxel,回傳命中骨 voxel 的數量""" nx, ny, nz = n dist = X * nx + Y * ny + Z * nz - d rx = (X - 2.0 * dist * nx).round().astype(np.int32) ry = (Y - 2.0 * dist * ny).round().astype(np.int32) rz = (Z - 2.0 * dist * nz).round().astype(np.int32) ok = (rx >= 0) & (rx < sx) & (ry >= 0) & (ry < sy) & (rz >= 0) & (rz < sz) if not ok.any(): return 0 return int(m[rz[ok], ry[ok], rx[ok]].sum()) def best_symmetry_plane(mask_zyx, phi_max=45.0, subsample=7, coarse_step=7.5, fine_step=1.0): """ 3D bone mask (z, y, x) 的最佳鏡稱面,一般平面方程 a·x + b·y + c·z = d (voxel index 座標;(a,b,c) 為單位法線,方向任意,不限制平行 YZ 面)。 以「每個 bone voxel 鏡射後四捨五入到最近 voxel 的命中率」為分數, 參數化 n = R_y(phi)·R_z(theta)·(1,0,0): theta : 法線在 axial (x,y) 平面內的旋轉 phi : 法線出平面的傾斜,限制在 [-phi_max, +phi_max] 以確保仍切分左右 搜尋:theta 由 2D axial 投影粗定位,再 3D 三段式(粗→細→微細) (粗/細階段用等距子樣 voxel 加速)。 回傳 dict: plane : (a, b, c, d) -> a*x + b*y + c*z = d normal : (a, b, c) offset : d theta_deg / phi_deg : 法線參數 ratio : 鏡射命中率(0..1) u, v : 平面內兩個正交方向(供繪製用) """ m = np.asarray(mask_zyx) > 0 sz, sy, sx = m.shape zz, yy, xx = np.nonzero(m) if xx.size < 100: n = np.array([1.0, 0.0, 0.0]) d = (sx - 1) / 2.0 return {'plane': (1.0, 0.0, 0.0, float(d)), 'normal': (1.0, 0.0, 0.0), 'offset': float(d), 'theta_deg': 0.0, 'phi_deg': 0.0, 'ratio': 1.0, 'u': (0.0, 1.0, 0.0), 'v': (0.0, 0.0, 1.0)} xf = xx.astype(np.float32) yf = yy.astype(np.float32) zf = zz.astype(np.float32) N = xf.size c0 = np.array([(sx - 1) / 2.0, (sy - 1) / 2.0, (sz - 1) / 2.0]) Xs, Ys, Zs = xf[::subsample], yf[::subsample], zf[::subsample] def n_of(theta_deg, phi_deg): t = np.deg2rad(theta_deg) p = np.deg2rad(phi_deg) return np.array([np.cos(t) * np.cos(p), np.sin(t), -np.cos(t) * np.sin(p)]) # theta 初值:2D axial 投影搜尋(垂直面情形) proj = m.max(axis=0) theta0 = best_symmetry_axis_angle(proj.astype(np.float32))[0] if proj.sum() >= 10 else 0.0 best = None def consider(theta, phi, d, full=False): nonlocal best n = n_of(theta, phi) X, Y, Z = (xf, yf, zf) if full else (Xs, Ys, Zs) s = _mirror_hit_count(X, Y, Z, n, d, m, sz, sy, sx) if best is None or s > best['score']: best = {'score': s, 'theta': float(theta), 'phi': float(phi), 'd': float(d)} # stage 1:粗搜尋(子樣) for th in np.arange(theta0 - coarse_step * 2, theta0 + coarse_step * 2 + 1e-9, coarse_step): for ph in np.arange(-phi_max, phi_max + 1e-9, coarse_step): n = n_of(th, ph) d0 = float(n @ c0) for dd in (-10.0, 0.0, 10.0): consider(th, ph, d0 + dd) # stage 2:細搜尋(子樣) for th in np.arange(best['theta'] - 2 * fine_step * 2, best['theta'] + 2 * fine_step * 2 + 1e-9, fine_step): for ph in np.arange(best['phi'] - 2 * fine_step * 2, best['phi'] + 2 * fine_step * 2 + 1e-9, fine_step): for dd in (-3.0, -1.0, 0.0, 1.0, 3.0): consider(th, ph, best['d'] + dd) # stage 3:微細搜尋(全分辨率) for th in np.arange(best['theta'] - fine_step, best['theta'] + fine_step + 1e-9, fine_step / 2): for ph in np.arange(best['phi'] - fine_step, best['phi'] + fine_step + 1e-9, fine_step / 2): for dd in (-1.0, -0.5, 0.0, 0.5, 1.0): consider(th, ph, best['d'] + dd, full=True) # stage 4:d 微調(全分辨率) b = best for dd in np.arange(-1.0, 1.0 + 1e-9, 0.25): consider(b['theta'], b['phi'], b['d'] + dd, full=True) n = n_of(best['theta'], best['phi']) theta = best['theta'] d = best['d'] if theta > 90.0 or theta < -90.0: # 正規化到 (-90, 90],法線翻轉時 d 取反 theta -= 180.0 n = -n d = -d ratio = _mirror_hit_count(xf, yf, zf, n, d, m, sz, sy, sx) / N u = np.cross(n, [0.0, 0.0, 1.0]) if np.linalg.norm(u) < 0.1: u = np.cross(n, [1.0, 0.0, 0.0]) u = u / np.linalg.norm(u) v = np.cross(n, u) return { 'plane': (float(n[0]), float(n[1]), float(n[2]), float(d)), 'normal': (float(n[0]), float(n[1]), float(n[2])), 'offset': float(d), 'theta_deg': float(theta), 'phi_deg': float(best['phi']), 'ratio': float(ratio), 'u': (float(u[0]), float(u[1]), float(u[2])), 'v': (float(v[0]), float(v[1]), float(v[2])), } def segment_spinous_process(mask_zyx, sym, band_frac=0.06, min_band=6.0, min_mass_frac=0.05): """ 以 best_symmetry_plane 的結果 sym 從 3D bone mask (z, y, x) 切出棘突。 棘突是中線後側構造,利用鏡稱面 a·x+b·y+c·z=d 定義: 1) 中線帶:骨 voxel 到平面的有號距離 |s| <= w, w = max(min_band, band_frac * s 全寬) 2) 前後方向:平面內兩軸 (u, v) 中 |y| 分量大者, 正規化成 +AP = 後側(本資料系 y 往前遞增,後側 = y 小側) 3) 中線帶的 AP 分佈呈兩大叢(椎體在前、椎弓/棘突在後), 以兩叢間的 AP 谷底為界,AP >= 谷底 的中線帶 voxel = 棘突(含中線椎弓); 無明顯谷底(如骨橋)fallback 取中線帶後側 15%。 回傳 (sp_mask (z,y,x) bool, ap_thresh, info dict); 資料過少時 sp_mask = None(info['mode'] 說明原因)。 """ m = np.asarray(mask_zyx) > 0 zz, yy, xx = np.nonzero(m) info = {'n_bone': int(zz.size), 'n_sp': 0, 'ap_thresh': None, 'band_w': None, 'mode': 'empty'} if zz.size < 50: return None, None, info a, b, c, d = sym['plane'] X = xx.astype(np.float64) Y = yy.astype(np.float64) Z = zz.astype(np.float64) s = X * a + Y * b + Z * c - d u = np.array(sym['u']) v = np.array(sym['v']) u_ap = u if abs(u[1]) >= abs(v[1]) else v if u_ap[1] > 0: u_ap = -u_ap # +AP = 後側(y 小側) w = max(float(min_band), float(band_frac) * float(s.max() - s.min())) mid = np.abs(s) <= w ap = X * u_ap[0] + Y * u_ap[1] + Z * u_ap[2] aps = ap[mid] info['band_w'] = float(w) if aps.size < 50: info['mode'] = 'too_few_midline' return None, None, info lo = int(np.floor(aps.min())) hi = int(np.ceil(aps.max())) th = None mode = 'fallback' if hi - lo >= 10: hist, edges = np.histogram(aps, bins=range(lo, hi + 1)) csum = np.concatenate([[0], np.cumsum(hist)]) total = csum[-1] peak = hist.max() best_i, best_score = None, -1.0 for i in range(len(hist)): if hist[i] >= 0.05 * peak: continue if csum[i] < min_mass_frac * total or (total - csum[i + 1]) < min_mass_frac * total: continue score = min(csum[i], total - csum[i + 1]) if score > best_score: best_score, best_i = score, i if best_i is not None: th = float(0.5 * (edges[best_i] + edges[best_i + 1])) mode = 'gap' if th is None: th = float(np.quantile(aps, 0.85)) sp_mask = np.zeros(m.shape, dtype=bool) sel = mid & (ap >= th) sp_mask[zz[sel], yy[sel], xx[sel]] = True info.update(n_sp=int(sel.sum()), ap_thresh=th, mode=mode) return sp_mask, th, info def best_upper_endplate_plane(mask_zyx, angle_max=45.0, thresh=3.0, n_iter=500, seed=42): """ 3D bone mask (z, y, x) 的最佳「上終板」近似平面 a·x + b·y + c·z = d (voxel index 座標;(a,b,c) 為朝上的單位法線)。 1) 每個 (y, x) 欄位取最上方 bone voxel 作為頂面點(僅前側半邊, y >= COM_y,避開後方元素,與 2D superior endplate 定義一致) 2) RANSAC 三點擬平面:法線限制在與 +z 軸 ≤ angle_max° 內, 計數 ±thresh voxel 內的頂面點為 inlier,取 inlier 最多者 3) SVD 最小二乘微調 回傳 dict(資料不足時回傳 None): plane : (a, b, c, d) normal / offset tilt_deg : 法線與 +z 軸的夾角(上終板傾斜) inlier_ratio : 頂面點落在平面 ±thresh 的比例 n_points / n_inliers u, v : 平面內正交方向(供繪製用) """ m = np.asarray(mask_zyx) > 0 nz, ny, nx = m.shape idx = np.where(m, np.arange(nz)[:, None, None], -1) ztop = idx.max(axis=0) # (y, x) 每欄最上 z y_split = int(round(center_of_mass(m)[1])) if m.sum() else 0 # ztop 是 (y, x):條件作用在 y 軸(axis 0) sel = (ztop >= 0) & (np.arange(ny)[:, None] >= y_split) yy, xx = np.where(sel) if xx.size < 8: return None P = np.stack((xx, yy, ztop[yy, xx]), axis=1).astype(np.float64) n = P.shape[0] rng = np.random.default_rng(seed) cos_min = np.cos(np.deg2rad(angle_max)) best_cnt, best_nv, best_d = -1, None, 0.0 for _ in range(n_iter): i, j, k = rng.choice(n, 3, replace=False) cr = np.cross(P[j] - P[i], P[k] - P[i]) ln = np.linalg.norm(cr) if ln < 1e-6: continue nv = cr / ln if nv[2] < 0: nv = -nv if nv[2] < cos_min: # 法線必須朝上 continue d = float(nv @ P[i]) cnt = int(np.count_nonzero(np.abs(P @ nv - d) <= thresh)) if cnt > best_cnt: best_cnt, best_nv, best_d = cnt, nv, d if best_nv is None: return None # SVD 微調 inl = P[np.abs(P @ best_nv - best_d) <= thresh] if inl.shape[0] < 3: return None mean = inl.mean(axis=0) _, _, Vt = np.linalg.svd(inl - mean, full_matrices=False) nv = Vt[2] if nv[2] < 0: nv = -nv d = float(nv @ mean) dist = np.abs(P @ nv - d) inl = P[dist <= thresh] u = np.cross(nv, [1.0, 0.0, 0.0]) u = u / np.linalg.norm(u) v = np.cross(nv, u) return { 'plane': (float(nv[0]), float(nv[1]), float(nv[2]), d), 'normal': (float(nv[0]), float(nv[1]), float(nv[2])), 'offset': d, 'tilt_deg': float(np.degrees(np.arccos(np.clip(nv[2], -1.0, 1.0)))), 'inlier_ratio': float(inl.shape[0] / n), 'n_points': int(n), 'n_inliers': int(inl.shape[0]), 'u': (float(u[0]), float(u[1]), float(u[2])), 'v': (float(v[0]), float(v[1]), float(v[2])), } def azimuth_rotation(image, show_plt=False, save_plt=False, output_path=None): img = sitk.ReadImage(image, sitk.sitkUInt8) arr_zyx = sitk.GetArrayFromImage(img) # (z, y, x) max_proj = np.max(arr_zyx, axis=0) # -> (y, x) binary_proj = (max_proj > 0).astype(np.uint8) ys, xs = np.where(binary_proj > 0) if len(xs) < 10: raise ValueError("Not enough foreground points") # 2) centroid ←←← 這裡一定會定義 cx, cy cy = ys.mean() cx = xs.mean() centroid = np.array([cy, cx]) cy = ys.mean() cx = xs.mean() centroid = np.array([cy, cx]) y_min = ys.min() top_row_mask = (ys == y_min) xs_top_row = xs[top_row_mask] # 取這一排的中位數或平均值 x_center = int(np.median(xs_top_row)) # 或用 np.mean() top_point = (y_min, x_center) # print(f"最上排中心點: {top_point}") # 計算從 top_point 到 centroid 的向量 dy = cy - y_min # y 方向的變化 dx = cx - x_center # x 方向的變化 # 計算與 y 軸的夾角 # 注意:影像座標系中 y 軸向下,所以要特別處理 angle_rad = np.arctan2(dx, dy) # 弧度 angle_deg = np.degrees(angle_rad) # 轉成角度 if show_plt: fig = plt.figure(figsize=(12, 12)) # 視覺化時加上角度資訊 plt.imshow(binary_proj, cmap='gray') plt.scatter(x_center, y_min, c='red', s=60, label='Top') plt.scatter(cx, cy, c='yellow', s=60, label='Centroid') plt.plot([x_center, cx], [y_min, cy], 'c-', lw=2, label=f'Angle with y-axis: {angle_deg:.1f}°') # 中矢狀面:最佳鏡稱面 a·x + b·y + c·z = d(法線方向任意,不平行 YZ 面) # 畫該平面在體積中央 z 切片上的截線 sym3 = best_symmetry_plane(arr_zyx) a3, b3, c3, d3 = sym3['plane'] zc_ = (arr_zyx.shape[0] - 1) / 2.0 rhs_ = d3 - c3 * zc_ # a*x + b*y = rhs n2d = np.hypot(a3, b3) x0_ = a3 * rhs_ / (n2d * n2d) y0_ = b3 * rhs_ / (n2d * n2d) u2_ = np.array([b3, -a3]) / n2d tfg_ = (xs - x0_) * u2_[0] + (ys - y0_) * u2_[1] L_ = float(np.abs(tfg_).max()) plt.plot([x0_ - L_ * u2_[0], x0_ + L_ * u2_[0]], [y0_ - L_ * u2_[1], y0_ + L_ * u2_[1]], color='magenta', lw=2, linestyle='--', label=f'Mirror plane: {a3:+.2f}x {b3:+.2f}y {c3:+.2f}z = {d3:.1f}') plt.legend() plt.title("Top point + centroid-directed line") plt.axis("off") if save_plt: if output_path is None: output_path = "azimuth_rotation.png" fig.savefig(output_path, dpi=200, bbox_inches="tight") plt.show() plt.close(fig) return angle_deg def split_spine_anterior_posterior(image_path, center_mode='com'): """ 從 sagittal view 看,沿著 y 軸(前後方向)將脊椎切成前半部和後半部 Parameters: image_path (str): 影像路徑 center_mode (str): 'com' 使用質心的 y 座標,'image' 使用圖片中心的 y 座標 Returns: anterior, posterior: 前半部和後半部的 binary mask """ # Sagittal projection: 沿著 x 軸投影 -> (z, y) img = sitk.ReadImage(image_path, sitk.sitkUInt8) arr_zyx = sitk.GetArrayFromImage(img) # Sagittal projection max_proj_sagittal = np.max(arr_zyx, axis=2) binary_proj = (max_proj_sagittal > 0).astype(np.uint8) # 決定切割的 y 座標 if center_mode == 'com': cz, cy = center_of_mass(binary_proj) split_y = int(round(cy)) label = f'Center of Mass (y={split_y})' elif center_mode == 'image': split_y = binary_proj.shape[1] // 2 label = f'Image Center (y={split_y})' # 檢查是否為數字,且範圍在 0 到 1 之間 (不含邊界) elif isinstance(center_mode, (int, float)) and 0 < center_mode < 1: ys = np.where(binary_proj > 0)[1] if ys.size == 0: # 額外保險:如果投影是空的 split_y = binary_proj.shape[1] // 2 else: y_min, y_max = ys.min(), ys.max() split_y = int(round(y_min + center_mode * (y_max - y_min))) label = f'Custom Ratio {center_mode} (y={split_y})' else: raise ValueError("center_mode 必須是 'com'、'image' 或介於 0 到 1 之間的浮點數 (例如 0.8)") # 切割:anterior (y < split_y) 和 posterior (y >= split_y) anterior = binary_proj.copy() posterior = binary_proj.copy() anterior[:, :split_y] = 0 # 保留spine前半部(image後半部)(y >= split_y) posterior[:, split_y:] = 0 # 保留spine後半部(image前半部)(y < split_y) return anterior, posterior, binary_proj def analyze_vertebral_tilt_contour(image_path, edge_type='superior', show_plot=False, debug=False, save_plt=False, output_path=None): """ 通過椎體前緣輪廓分析傾斜(可選上或下終板) Parameters: edge_type: 'superior' 上終板, 'inferior' 下終板, 'both' 兩者都分析 """ # 切割出 anterior 部分 anterior, posterior, binary_proj = split_spine_anterior_posterior(image_path, center_mode='com') zs, ys = np.where(anterior > 0) if len(zs) == 0: return None from sklearn.linear_model import RANSACRegressor results = {} # === 根據 edge_type 決定要分析哪些邊 === edges_to_analyze = [] if edge_type == 'superior' or edge_type == 'both': edges_to_analyze.append('superior') if edge_type == 'inferior' or edge_type == 'both': edges_to_analyze.append('inferior') all_edge_points = {} all_inliers = {} all_outliers = {} all_slopes = {} all_intercepts = {} all_angles = {} for edge in edges_to_analyze: # 對每個 y,找對應的邊緣點 edge_points = [] unique_ys = np.unique(ys) for y in unique_ys: z_at_y = zs[ys == y] if edge == 'superior': z_edge = z_at_y.max() # 最上面的點(z 最小) else: # inferior z_edge = z_at_y.min() # 最下面的點(z 最大) edge_points.append([y, z_edge]) edge_points = np.array(edge_points) all_edge_points[edge] = edge_points if len(edge_points) < 10: continue # RANSAC 擬合 X = edge_points[:, 0].reshape(-1, 1) y_data = edge_points[:, 1] ransac = RANSACRegressor( residual_threshold=5.0, random_state=42 ) ransac.fit(X, y_data) inlier_mask = ransac.inlier_mask_ outlier_mask = ~inlier_mask edge_points_inliers = edge_points[inlier_mask] edge_points_outliers = edge_points[outlier_mask] all_inliers[edge] = edge_points_inliers all_outliers[edge] = edge_points_outliers # 獲取擬合結果 slope = ransac.estimator_.coef_[0] intercept = ransac.estimator_.intercept_ all_slopes[edge] = slope all_intercepts[edge] = intercept # 計算 R² y_pred = ransac.predict(edge_points_inliers[:, 0].reshape(-1, 1)) ss_res = np.sum((edge_points_inliers[:, 1] - y_pred) ** 2) ss_tot = np.sum((edge_points_inliers[:, 1] - np.mean(edge_points_inliers[:, 1])) ** 2) r_squared = 1 - (ss_res / ss_tot) if ss_tot > 0 else 0 # 計算傾斜角度 tilt_angle = np.degrees(np.arctan(slope)) all_angles[edge] = tilt_angle if debug: print(f"\n=== {edge.upper()} ENDPLATE ===") print(f"Total points: {len(edge_points)}") print(f"Inliers: {len(edge_points_inliers)}") print(f"Outliers: {len(edge_points_outliers)}") print(f"{edge.capitalize()} 終板傾斜角度: {tilt_angle:.2f}°") print(f"斜率: {slope:.4f}, R²: {r_squared:.4f}") results[edge] = { 'tilt_angle_deg': tilt_angle, 'slope': slope, 'intercept': intercept, 'r_squared': r_squared, 'n_inliers': len(edge_points_inliers), 'n_outliers': len(edge_points_outliers) } # Visualization if show_plot: n_edges = len(edges_to_analyze) fig, axes = plt.subplots(n_edges, 2, figsize=(16, 6*n_edges)) if n_edges == 1: axes = axes.reshape(1, -1) colors = {'superior': 'red', 'inferior': 'cyan'} for idx, edge in enumerate(edges_to_analyze): edge_points = all_edge_points[edge] edge_points_inliers = all_inliers[edge] edge_points_outliers = all_outliers[edge] slope = all_slopes[edge] intercept = all_intercepts[edge] tilt_angle = all_angles[edge] color = colors[edge] # 左圖:scatter plot ax_left = axes[idx, 0] if len(edge_points_outliers) > 0: ax_left.scatter(edge_points_outliers[:, 0], edge_points_outliers[:, 1], c='lightcoral', s=30, alpha=0.6, marker='x', label=f'Outliers ({len(edge_points_outliers)})', zorder=3) ax_left.scatter(edge_points_inliers[:, 0], edge_points_inliers[:, 1], c=color, s=20, alpha=0.7, label=f'Inliers ({len(edge_points_inliers)})', zorder=4) # 擬合線 y_line = np.array([edge_points[:, 0].min(), edge_points[:, 0].max()]) z_line = slope * y_line + intercept ax_left.plot(y_line, z_line, 'lime', linewidth=3, label=f'Angle: {tilt_angle:.1f}°\nR²: {results[edge]["r_squared"]:.3f}', zorder=5) ax_left.set_xlabel('y') ax_left.set_ylabel('z') ax_left.set_title(f'{edge.capitalize()} Endplate Analysis\nTilt: {tilt_angle:.1f}°') ax_left.invert_yaxis() ax_left.legend() ax_left.grid(True, alpha=0.3) # 右圖:原始影像 ax_right = axes[idx, 1] ax_right.imshow(anterior, cmap='gray', aspect='equal') if len(edge_points_outliers) > 0: ax_right.scatter(edge_points_outliers[:, 0], edge_points_outliers[:, 1], c='red', s=40, alpha=0.7, marker='x', label='Outliers', zorder=4) ax_right.scatter(edge_points_inliers[:, 0], edge_points_inliers[:, 1], c=color, s=25, alpha=0.8, label='Inliers', zorder=3) ax_right.plot(y_line, z_line, 'lime', linewidth=3, linestyle='--', label=f'{edge.capitalize()}: {tilt_angle:.1f}°', zorder=5) ax_right.set_title(f'Anterior Half - {edge.capitalize()} Edge') ax_right.set_xlabel('y') ax_right.set_ylabel('z') ax_right.invert_yaxis() ax_right.legend() plt.tight_layout() if save_plt: if output_path is None: output_path = "analyze_vertebral_tilt_contour.png" fig.savefig(output_path, dpi=200, bbox_inches="tight") plt.show() plt.close(fig) return results