perf(track): use sum()/len() instead of np.mean in average_boxes (#23521)

* perf(track): avoid numpy reductions on tiny box lists in position smoothing

update_position runs per tracked object per frame. While a position has
fewer than 10 samples it calls np.percentile four times, and average_boxes
(per stationary object per frame) calls np.mean four times - all on lists of
at most 10 ints, where numpy's per-call dispatch/validation overhead
dominates the actual work.

Replace them with pure-Python equivalents:
- average_boxes: sum()/len() instead of np.mean (bit-identical output)
- interpolated_percentile(): linear-interpolated percentile matching
  numpy.percentile (including its lerp branch at frac>=0.5) for the small
  lists used here, in place of np.percentile

Measured in the release image (numpy 1.26.4) on a 10-element list:
np.percentile 18735 ns -> 191 ns/call (98x); np.mean-based average_boxes
7480 ns -> 591 ns (12.7x); ~74 us saved per object-frame in update_position.
A live py-spy --gil profile of a camera process_frames worker showed
np.percentile (update_position) and np.mean (average_boxes) among the top
Frigate-owned on-CPU frames.

Output is unchanged: added tests assert both helpers are bit-identical to
numpy over randomized small inputs.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

* Drop interpolated_percentile, keep only average_boxes

Per review: reimplementing np.percentile hurts readability and risks
divergence from numpy (e.g. numpy 2.x). Revert update_position to
np.percentile and remove the helper; keep only the average_boxes change
(sum()/len() instead of np.mean), which stays bit-identical.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

---------

Co-authored-by: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

frigate/test/test_obects.py

@@ -1,6 +1,22 @@
+import random
 import unittest
 
+import numpy as np
+
 from frigate.track.tracked_object import TrackedObjectAttribute
+from frigate.util.object import average_boxes
+
+
+class TestBoxStatistics(unittest.TestCase):
+    def test_average_boxes_matches_numpy(self) -> None:
+        rng = random.Random(0)
+        for _ in range(5000):
+            boxes = [
+                [rng.randint(0, 4000) for _ in range(4)]
+                for _ in range(rng.randint(1, 10))
+            ]
+            expected = [float(np.mean([b[i] for b in boxes])) for i in range(4)]
+            self.assertEqual(average_boxes(boxes), expected)
 
 
 class TestAttribute(unittest.TestCase):

frigate/util/object.py

@@ -339,18 +339,13 @@ def reduce_boxes(boxes, iou_threshold=0.0):
 
 def average_boxes(boxes: list[list[int, int, int, int]]) -> list[int, int, int, int]:
     """Return a box that is the average of a list of boxes."""
-    x_mins = []
-    y_mins = []
-    x_max = []
-    y_max = []
-
-    for box in boxes:
-        x_mins.append(box[0])
-        y_mins.append(box[1])
-        x_max.append(box[2])
-        y_max.append(box[3])
-
-    return [np.mean(x_mins), np.mean(y_mins), np.mean(x_max), np.mean(y_max)]
+    n = len(boxes)
+    return [
+        sum(box[0] for box in boxes) / n,
+        sum(box[1] for box in boxes) / n,
+        sum(box[2] for box in boxes) / n,
+        sum(box[3] for box in boxes) / n,
+    ]
 
 
 def median_of_boxes(boxes: list[list[int, int, int, int]]) -> list[int, int, int, int]: