[proto] Small optim for perspective op on images (#6907)

* [proto] small optim for perspective op on images, reverted concat trick on bboxes

* revert unrelated changes

* PR review updates

* PR review change

torchvision/prototype/transforms/functional/_geometry.py

@@ -907,6 +907,36 @@ def crop(inpt: features.InputTypeJIT, top: int, left: int, height: int, width: i
         return crop_image_pil(inpt, top, left, height, width)
 
 
+def _perspective_grid(coeffs: List[float], ow: int, oh: int, dtype: torch.dtype, device: torch.device) -> torch.Tensor:
+    # https://github.com/python-pillow/Pillow/blob/4634eafe3c695a014267eefdce830b4a825beed7/
+    # src/libImaging/Geometry.c#L394
+
+    #
+    # 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)
+    #
+
+    theta1 = torch.tensor(
+        [[[coeffs[0], coeffs[1], coeffs[2]], [coeffs[3], coeffs[4], coeffs[5]]]], dtype=dtype, device=device
+    )
+    theta2 = torch.tensor([[[coeffs[6], coeffs[7], 1.0], [coeffs[6], coeffs[7], 1.0]]], dtype=dtype, device=device)
+
+    d = 0.5
+    base_grid = torch.empty(1, oh, ow, 3, dtype=dtype, device=device)
+    x_grid = torch.linspace(d, ow * 1.0 + d - 1.0, steps=ow, device=device)
+    base_grid[..., 0].copy_(x_grid)
+    y_grid = torch.linspace(d, oh * 1.0 + d - 1.0, steps=oh, device=device).unsqueeze_(-1)
+    base_grid[..., 1].copy_(y_grid)
+    base_grid[..., 2].fill_(1)
+
+    rescaled_theta1 = theta1.transpose(1, 2).div_(torch.tensor([0.5 * ow, 0.5 * oh], dtype=dtype, device=device))
+    output_grid1 = base_grid.view(1, oh * ow, 3).bmm(rescaled_theta1)
+    output_grid2 = base_grid.view(1, oh * ow, 3).bmm(theta2.transpose(1, 2))
+
+    output_grid = output_grid1.div_(output_grid2).sub_(1.0)
+    return output_grid.view(1, oh, ow, 2)
+
+
 def _perspective_coefficients(
     startpoints: Optional[List[List[int]]],
     endpoints: Optional[List[List[int]]],
@@ -944,7 +974,19 @@ def perspective_image_tensor(
     else:
         needs_unsquash = False
 
-    output = _FT.perspective(image, perspective_coeffs, interpolation=interpolation.value, fill=fill)
+    _FT._assert_grid_transform_inputs(
+        image,
+        matrix=None,
+        interpolation=interpolation.value,
+        fill=fill,
+        supported_interpolation_modes=["nearest", "bilinear"],
+        coeffs=perspective_coeffs,
+    )
+
+    ow, oh = image.shape[-1], image.shape[-2]
+    dtype = image.dtype if torch.is_floating_point(image) else torch.float32
+    grid = _perspective_grid(perspective_coeffs, ow=ow, oh=oh, dtype=dtype, device=image.device)
+    output = _FT._apply_grid_transform(image, grid, interpolation.value, fill=fill)
 
     if needs_unsquash:
         output = output.reshape(shape)
@@ -1012,16 +1054,16 @@ def perspective_bounding_box(
         (-perspective_coeffs[0] * perspective_coeffs[7] + perspective_coeffs[1] * perspective_coeffs[6]) / denom,
     ]
 
-    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],
-        ],
+    theta1 = torch.tensor(
+        [[inv_coeffs[0], inv_coeffs[1], inv_coeffs[2]], [inv_coeffs[3], inv_coeffs[4], inv_coeffs[5]]],
         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
@@ -1032,9 +1074,8 @@ 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_denom_points = torch.matmul(points, theta12_T)
-    numer_points = numer_denom_points[:, :2]
-    denom_points = numer_denom_points[:, 2:]
+    numer_points = torch.matmul(points, theta1.T)
+    denom_points = torch.matmul(points, theta2.T)
     transformed_points = numer_points.div_(denom_points)
 
     # 3) Reshape transformed points to [N boxes, 4 points, x/y coords]