【深入pytorch】transforms.functional 梯度流动问题

实验环境：

torch.__version__
Out[3]: '1.12.1+cu113'

首先测试一下：

import torch
from torchvision.transforms import functional as F
from torch.autograd import Function
img = torch.randn(1, 3, 224, 224)
startpoints = torch.FloatTensor([[0., 0.], [0., 224.], [224., 0.], [224., 224.]])
endpoints = torch.FloatTensor([[0., 0.], [0., 200.], [200., 0.], [200., 200.]])
t = F.perspective(img, startpoints, endpoints)
print(t.requires_grad)

没有梯度

查看源码torchvision.transforms.functional.perspective，是transform的对外接口，负责处理输入数据类型等问题，

def perspective(
    img: Tensor,
    startpoints: List[List[int]],
    endpoints: List[List[int]],
    interpolation: InterpolationMode = InterpolationMode.BILINEAR,
    fill: Optional[List[float]] = None,
) -> Tensor:
    """Perform perspective transform of the given image.
    If the image is torch Tensor, it is expected
    to have [..., H, W] shape, where ... means an arbitrary number of leading dimensions.

    Args:
        img (PIL Image or Tensor): Image to be transformed.
        startpoints (list of list of ints): List containing four lists of two integers corresponding to four corners
            ``[top-left, top-right, bottom-right, bottom-left]`` of the original image.
        endpoints (list of list of ints): List containing four lists of two integers corresponding to four corners
            ``[top-left, top-right, bottom-right, bottom-left]`` of the transformed image.
        interpolation (InterpolationMode): Desired interpolation enum defined by
            :class:`torchvision.transforms.InterpolationMode`. Default is ``InterpolationMode.BILINEAR``.
            If input is Tensor, only ``InterpolationMode.NEAREST``, ``InterpolationMode.BILINEAR`` are supported.
            For backward compatibility integer values (e.g. ``PIL.Image[.Resampling].NEAREST``) are still accepted,
            but deprecated since 0.13 and will be removed in 0.15. Please use InterpolationMode enum.
        fill (sequence or number, optional): Pixel fill value for the area outside the transformed
            image. If given a number, the value is used for all bands respectively.

            .. note::
                In torchscript mode single int/float value is not supported, please use a sequence
                of length 1: ``[value, ]``.

    Returns:
        PIL Image or Tensor: transformed Image.
    """
    if not torch.jit.is_scripting() and not torch.jit.is_tracing():
        _log_api_usage_once(perspective)

    coeffs = _get_perspective_coeffs(startpoints, endpoints)

    # Backward compatibility with integer value
    if isinstance(interpolation, int):
        warnings.warn(
            "Argument 'interpolation' of type int is deprecated since 0.13 and will be removed in 0.15. "
            "Please use InterpolationMode enum."
        )
        interpolation = _interpolation_modes_from_int(interpolation)

    if not isinstance(interpolation, InterpolationMode):
        raise TypeError("Argument interpolation should be a InterpolationMode")

    if not isinstance(img, torch.Tensor):
        pil_interpolation = pil_modes_mapping[interpolation]
        return F_pil.perspective(img, coeffs, interpolation=pil_interpolation, fill=fill)

    return F_t.perspective(img, coeffs, interpolation=interpolation.value, fill=fill)

继续看torchvision.transforms.functional_tensor.perspective，是tensor版本的功能性函数接口。

调用 _perspective_grid 函数生成透视变换的栅格

调用 _apply_grid_transform 函数，将生成的栅格应用到原始图像上，执行透视变换

def perspective(
    img: Tensor, perspective_coeffs: List[float], interpolation: str = "bilinear", fill: Optional[List[float]] = None
) -> Tensor:
    if not (isinstance(img, torch.Tensor)):
        raise TypeError("Input img should be Tensor.")

    _assert_image_tensor(img)

    _assert_grid_transform_inputs(
        img,
        matrix=None,
        interpolation=interpolation,
        fill=fill,
        supported_interpolation_modes=["nearest", "bilinear"],
        coeffs=perspective_coeffs,
    )

    ow, oh = img.shape[-1], img.shape[-2]
    dtype = img.dtype if torch.is_floating_point(img) else torch.float32
    grid = _perspective_grid(perspective_coeffs, ow=ow, oh=oh, dtype=dtype, device=img.device)
    return _apply_grid_transform(img, grid, interpolation, fill=fill)

其中：_apply_grid_transform 在给定的网格上对图像进行变换。将输入图像转换为与网格相同的数据类型，进行填充色处理。

def _apply_grid_transform(img: Tensor, grid: Tensor, mode: str, fill: Optional[List[float]]) -> Tensor:

    img, need_cast, need_squeeze, out_dtype = _cast_squeeze_in(img, [grid.dtype])

    if img.shape[0] > 1:
        # Apply same grid to a batch of images
        grid = grid.expand(img.shape[0], grid.shape[1], grid.shape[2], grid.shape[3])

    # Append a dummy mask for customized fill colors, should be faster than grid_sample() twice
    if fill is not None:
        dummy = torch.ones((img.shape[0], 1, img.shape[2], img.shape[3]), dtype=img.dtype, device=img.device)
        img = torch.cat((img, dummy), dim=1)

    img = grid_sample(img, grid, mode=mode, padding_mode="zeros", align_corners=False)

    # Fill with required color
    if fill is not None:
        mask = img[:, -1:, :, :]  # N * 1 * H * W
        img = img[:, :-1, :, :]  # N * C * H * W
        mask = mask.expand_as(img)
        len_fill = len(fill) if isinstance(fill, (tuple, list)) else 1
        fill_img = torch.tensor(fill, dtype=img.dtype, device=img.device).view(1, len_fill, 1, 1).expand_as(img)
        if mode == "nearest":
            mask = mask < 0.5
            img[mask] = fill_img[mask]
        else:  # 'bilinear'
            img = img * mask + (1.0 - mask) * fill_img

    img = _cast_squeeze_out(img, need_cast, need_squeeze, out_dtype)
    return img

提到 grid生成

生成一个透视栅格，输入参数是透视变换的系数（coeffs）、输出图像的宽度（ow）和高度（oh）。theta1和theta2，用于计算变换后的 x 和 y 坐标。创建一个基础栅格（base_grid），其中包含输出图像的所有像素位置。基础栅格与theta1和theta2进行矩阵乘法操作，生成变换后的位置。

def _perspective_grid(coeffs: List[float], ow: int, oh: int, dtype: torch.dtype, device: torch.device) -> 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) / 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 / output_grid2 - 1.0
    return output_grid.view(1, oh, ow, 2)

探索

https://github.com/python-pillow/Pillow/blob/4634eafe3c695a014267eefdce830b4a825beed7/src/libImaging/Geometry.c#L394

可梯度方式

https://github.com/pytorch/vision/pull/7925

在torchvision.transforms.functional_tensor._perspective_grid中修改

    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)
    # 修改这两句，试图可微分
    theta1 = torch.reshape(coeffs[:6], (1, 2, 3)).to(dtype=dtype, device=device)
    theta2 = torch.reshape(torch.cat(
        (coeffs[6:], torch.ones(1, device=coeffs.device))), (1, 1, 3)).expand(-1, 2, -1).to(dtype=dtype, device=device)

修改后报错：

C:\conda\envs\CUDA110_torch\lib\site-packages\torchvision\transforms\functional.py:629: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).
  b_matrix = torch.tensor(startpoints, dtype=torch.float).view(8)
Traceback (most recent call last):
  File "C:\conda\envs\CUDA110_torch\lib\site-packages\IPython\core\interactiveshell.py", line 3505, in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)
  File "<ipython-input-3-087b1cddce7b>", line 1, in <module>
    F.perspective(img, startpoints, endpoints)
  File "C:\conda\envs\CUDA110_torch\lib\site-packages\torchvision\transforms\functional.py", line 688, in perspective
    return F_t.perspective(img, coeffs, interpolation=interpolation.value, fill=fill)
  File "C:\conda\envs\CUDA110_torch\lib\site-packages\torchvision\transforms\functional_tensor.py", line 748, in perspective
    grid = _perspective_grid(perspective_coeffs, ow=ow, oh=oh, dtype=dtype, device=img.device)
  File "C:\conda\envs\CUDA110_torch\lib\site-packages\torchvision\transforms\functional_tensor.py", line 709, in _perspective_grid
    theta1 = torch.reshape(coeffs[:6], (1, 2, 3)).to(dtype=dtype, device=device)
TypeError: reshape(): argument 'input' (position 1) must be Tensor, not list

修改为：

theta1 = torch.reshape(torch.tensor(coeffs[:6]), (1, 2, 3)).to(dtype=dtype, device=device)

报错

C:\conda\envs\CUDA110_torch\python.exe D:\myGit\ipad_attack\mydata\test_torch自带的transform丢失梯度问题.py 
C:\conda\envs\CUDA110_torch\lib\site-packages\torchvision\transforms\functional.py:629: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).
  b_matrix = torch.tensor(startpoints, dtype=torch.float).view(8)
Traceback (most recent call last):
  File "D:\myGit\ipad_attack\mydata\test_torch自带的transform丢失梯度问题.py", line 30, in <module>
    t = F.perspective(img, startpoints, endpoints)
  File "C:\conda\envs\CUDA110_torch\lib\site-packages\torchvision\transforms\functional.py", line 688, in perspective
    return F_t.perspective(img, coeffs, interpolation=interpolation.value, fill=fill)
  File "C:\conda\envs\CUDA110_torch\lib\site-packages\torchvision\transforms\functional_tensor.py", line 748, in perspective
    grid = _perspective_grid(perspective_coeffs, ow=ow, oh=oh, dtype=dtype, device=img.device)
  File "C:\conda\envs\CUDA110_torch\lib\site-packages\torchvision\transforms\functional_tensor.py", line 711, in _perspective_grid
    (coeffs[6:], torch.ones(1, device=coeffs.device))), (1, 1, 3)).expand(-1, 2, -1).to(dtype=dtype, device=device)
AttributeError: 'list' object has no attribute 'device'

Process finished with exit code 1

打印coeffs：

[1.1200001239776611,
 2.2111888142717362e-07,
 -2.181137097068131e-05,
 -2.3566984452827455e-07,
 1.1200006008148193,
 9.300353667640593e-06,
 -5.271598157996493e-10,
 1.9876917889405377e-09]

修改为：

运行测试代码：

import torch
from torchvision.transforms import functional as F
from torch.autograd import Function
img = torch.randn(1, 3, 224, 224)
startpoints = torch.tensor([[0., 0.], [0., 224.], [224., 0.], [224., 224.]], requires_grad=True)
endpoints = torch.tensor([[0., 0.], [0., 200.], [200., 0.], [200., 200.]], requires_grad=True)

print(startpoints.requires_grad)
t = F.perspective(img, startpoints, endpoints)
y = t**3
y.backward()
print(t.requires_grad,y)

发现：

C:\conda\envs\CUDA110_torch\lib\site-packages\torchvision\transforms\functional.py:629: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).
  b_matrix = torch.tensor(startpoints, dtype=torch.float).view(8)
Traceback (most recent call last):
  File "D:\myGit\ipad_attack\mydata\test_torch自带的transform丢失梯度问题.py", line 33, in <module>
    t.backward()
  File "C:\conda\envs\CUDA110_torch\lib\site-packages\torch\_tensor.py", line 396, in backward
    torch.autograd.backward(self, gradient, retain_graph, create_graph, inputs=inputs)
  File "C:\conda\envs\CUDA110_torch\lib\site-packages\torch\autograd\__init__.py", line 173, in backward
    Variable._execution_engine.run_backward(  # Calls into the C++ engine to run the backward pass
RuntimeError: element 0 of tensors does not require grad and does not have a grad_fn

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
Cell In[12], line 11
      9 t = F.perspective(img, startpoints, endpoints)
     10 y = t**3
---> 11 y.backward()
     12 print(t.requires_grad,y)

File C:\conda\envs\CUDA110_torch\lib\site-packages\torch\_tensor.py:396, in Tensor.backward(self, gradient, retain_graph, create_graph, inputs)
    387 if has_torch_function_unary(self):
    388     return handle_torch_function(
    389         Tensor.backward,
    390         (self,),
   (...)
    394         create_graph=create_graph,
    395         inputs=inputs)
--> 396 torch.autograd.backward(self, gradient, retain_graph, create_graph, inputs=inputs)

File C:\conda\envs\CUDA110_torch\lib\site-packages\torch\autograd\__init__.py:173, in backward(tensors, grad_tensors, retain_graph, create_graph, grad_variables, inputs)
    168     retain_graph = create_graph
    170 # The reason we repeat same the comment below is that
    171 # some Python versions print out the first line of a multi-line function
    172 # calls in the traceback and some print out the last line
--> 173 Variable._execution_engine.run_backward(  # Calls into the C++ engine to run the backward pass
    174     tensors, grad_tensors_, retain_graph, create_graph, inputs,
    175     allow_unreachable=True, accumulate_grad=True)

RuntimeError: element 0 of tensors does not require grad and does not have a grad_fn