diff --git a/tests/test_convex_hull.py b/tests/test_convex_hull.py
index 4c16033..24c8436 100644
--- a/tests/test_convex_hull.py
+++ b/tests/test_convex_hull.py
@@ -9,6 +9,10 @@
 from imops.src._convex_hull import _left_right_bounds, _offset_unique
 
 
+np.random.seed(1337)
+N_STRESS = 250
+
+
 @pytest.fixture(params=[False, True])
 def offset_coordinates(request):
     return request.param
@@ -60,7 +64,26 @@ def test_convex_hull_image(offset_coordinates):
     assert (chull >= image).all()
     assert (chull >= chull_ref).all()
 
-    assert ((chull > chull_ref).sum() / chull_ref.sum()) < 1e-2
+    assert ((chull > chull_ref).sum() / chull_ref.sum()) < 2e-2
+
+
+def test_convex_hull_image_random(offset_coordinates):
+    for _ in range(N_STRESS):
+        image = np.zeros((200, 200), dtype=bool)
+
+        image[30:-30, 20:-40] = np.random.randn(140, 140) > 2
+
+        try:
+            chull_ref = convex_hull_image(image, offset_coordinates=offset_coordinates, include_borders=True)
+        except TypeError:
+            chull_ref = convex_hull_image(image, offset_coordinates=offset_coordinates)
+
+        chull = convex_hull_image_fast(image, offset_coordinates=offset_coordinates)
+
+        assert (chull >= image).all()
+        assert (chull >= chull_ref).all()
+
+        assert ((chull > chull_ref).sum() / chull_ref.sum()) < 2e-2
 
 
 def test_convex_hull_image_non2d(offset_coordinates):