I believe you can achieve this by applying grid sampling on your original input and using a grid to guide the sampling process. If you take a coordinate grid of your image and sample using that the resulting image will be equal to the original image. However you can apply a shift on this grid and therefore sample with the given shift. Grid sampling works with floating-point grids of course, which means you can apply an arbitrary non-round shift to your image and choose a sampling mode (bilinear is the default).
This can be implemented out of the box with F.grid_sampling. Given an image tensor img, we first construct a pixel grid of that image using torch.meshgrid. Keep in mind the grid used by the sampler must be normalized to [-1, -1]. Therefore pixel x=0,y=0 should be mapped to (-1,-1), pixel x=w,y=h mapped to (1,1), and the center pixel will end up at around (0,0).
Use two torch.arange with a [0,1]-normalization followed by a remapping to [-1,1]:
>>> c,h,w = img.shape
>>> x, y = torch.arange(h)/(h-1), torch.arange(w)/(w-1)
>>> grid = torch.dstack(torch.meshgrid(x, y))*2-1
So the resulting grid has a shape of (c, h, w) which will be the dimensions of the output image produced by the sampling process.
Since we are not working with batched elements, we need to unsqueeze singleton dimensions on both img and grid. Then we can apply F.grid_sample:
>>> sampled = F.grid_sample(img[None], grid[None])
Following this you can apply your arbitrary mu_x, mu_y shift and even easily use this to batches of images and shifts. The way you would define your sampling is by defining a shifted grid:
>>> x_s, y_s = (torch.arange(h)+mu_y)/(h-1), (torch.arange(w)+mu_x)/(w-1)
Where mu_x and mu_y are the values in pixels (floating point) with wish which the image is shifted on the horizontal and vertical axes respectively. To acquire the sampled image, apply F.grid_sampling on a grid made up of x_s and y_s:
>>> grid_shifted = torch.dstack(torch.meshgrid(x_s, y_s))*2-1
>>> sampled = F.grid_sample(img[None], grid_shifted[None])
