[proto] Small optims for perspective bboxes op (#6891)

* [proto] Speed-up crop on bboxes and tests

* Fix linter

* Update _geometry.py

* Fixed device issue

* Revert changes in test/prototype_transforms_kernel_infos.py

* Fixed failing correctness tests

* [proto] Optimized functional pad op for bboxes + tests

* Renamed copy-pasted variable name

* [proto] Small optims for perspective bboxes op

torchvision/prototype/transforms/functional/_geometry.py

@@ -928,16 +928,16 @@ def perspective_bounding_box(
         (-perspective_coeffs[0] * perspective_coeffs[7] + perspective_coeffs[1] * perspective_coeffs[6]) / denom,
     ]
 
-    theta1 = torch.tensor(
-        [[inv_coeffs[0], inv_coeffs[1], inv_coeffs[2]], [inv_coeffs[3], inv_coeffs[4], inv_coeffs[5]]],
+    theta12_T = torch.tensor(
+        [
+            [inv_coeffs[0], inv_coeffs[3], inv_coeffs[6], inv_coeffs[6]],
+            [inv_coeffs[1], inv_coeffs[4], inv_coeffs[7], inv_coeffs[7]],
+            [inv_coeffs[2], inv_coeffs[5], 1.0, 1.0],
+        ],
         dtype=dtype,
         device=device,
     )
 
-    theta2 = torch.tensor(
-        [[inv_coeffs[6], inv_coeffs[7], 1.0], [inv_coeffs[6], inv_coeffs[7], 1.0]], dtype=dtype, device=device
-    )
-
     # 1) Let's transform bboxes into a tensor of 4 points (top-left, top-right, bottom-left, bottom-right corners).
     # Tensor of points has shape (N * 4, 3), where N is the number of bboxes
     # Single point structure is similar to
@@ -948,15 +948,16 @@ def perspective_bounding_box(
     #   x_out = (coeffs[0] * x + coeffs[1] * y + coeffs[2]) / (coeffs[6] * x + coeffs[7] * y + 1)
     #   y_out = (coeffs[3] * x + coeffs[4] * y + coeffs[5]) / (coeffs[6] * x + coeffs[7] * y + 1)
 
-    numer_points = torch.matmul(points, theta1.T)
-    denom_points = torch.matmul(points, theta2.T)
-    transformed_points = numer_points / denom_points
+    numer_denom_points = torch.matmul(points, theta12_T)
+    numer_points = numer_denom_points[:, :2]
+    denom_points = numer_denom_points[:, 2:]
+    transformed_points = numer_points.div_(denom_points)
 
     # 3) Reshape transformed points to [N boxes, 4 points, x/y coords]
     # and compute bounding box from 4 transformed points:
     transformed_points = transformed_points.reshape(-1, 4, 2)
-    out_bbox_mins, _ = torch.min(transformed_points, dim=1)
-    out_bbox_maxs, _ = torch.max(transformed_points, dim=1)
+    out_bbox_mins, out_bbox_maxs = torch.aminmax(transformed_points, dim=1)
+
     out_bboxes = torch.cat([out_bbox_mins, out_bbox_maxs], dim=1).to(bounding_box.dtype)
 
     # out_bboxes should be of shape [N boxes, 4]