diff --git a/apps/worker/video_processing/dedup.py b/apps/worker/video_processing/dedup.py
index d5f389095..469a9cc30 100755
--- a/apps/worker/video_processing/dedup.py
+++ b/apps/worker/video_processing/dedup.py
@@ -277,6 +277,9 @@ class VideoDeduplicator:
     def _bhattacharyya_coefficient(hist_a: list[float], hist_b: list[float]) -> float:
         """Bhattacharyya 系数：Σ √(a[i] * b[i])，范围 [0, 1]，1=完全相同。
 
+        直方图值均为非负浮点数，用 ``x ** 0.5`` 替代 ``np.sqrt``，
+        避免在此纯标量计算中引入对 numpy 的额外依赖。
+
         Args:
             hist_a: 第一组直方图数据
             hist_b: 第二组直方图数据
@@ -287,7 +290,7 @@ class VideoDeduplicator:
         min_len = min(len(hist_a), len(hist_b))
         a = hist_a[:min_len]
         b = hist_b[:min_len]
-        return float(sum(np.sqrt(ai * bi) for ai, bi in zip(a, b)))
+        return float(sum((ai * bi) ** 0.5 for ai, bi in zip(a, b)))
 
     @staticmethod
     def _compute_histogram_similarity(