How can I create accurate image masks from Graphics?

Question

I am looking to generate image masks using Graphics. For this, the requirements are that:

1. The rasterized mask must have the exact same dimensions as the image with which it will be used.
2. The image coordinates system (as described in the documentation of ImageValue, under Details) must line up perfectly with the Graphics coordinate system.

Neither seems to work readily.

Mask has an incorrect size

dims = {20, 20};

mask = Rasterize[
  Graphics[{},
   PlotRange -> Transpose[{{0, 0}, dims}], ImageSize -> dims,
   PlotRangePadding -> None
  ],
  ImageResolution -> 72
 ]

The mask is of the wrong size. ImageDimensions[mask] gives {20, 22}.

Coordinates don't line up

Example code:

dims = {21, 21};

pix = Image@ReplacePart[ConstantArray[0, dims], {{11, 11}} -> 1]

mask = Rasterize[
  Graphics[{Disk[dims/2, 6]},
   PlotRange -> Transpose[{{0, 0}, dims}], ImageSize -> dims,
   PlotRangePadding -> None
  ],
  ImageResolution -> 72
 ]

The image size is odd, so there is a middle pixel. pix visualizes this pixel. mask draws a disk around it. But the pixel is clearly not in the middle of the disk:

Magnify[mask + pix, 5]

Attempted workarounds

• ImageMargins -> 0, ImagePadding -> None does not help.
• Adding ImageSize to Rasterize as well, in addition to Graphics, does not help.
• RasterSize can force a specific image size, but it does not help with alignment

System information

Mathematica 13.0.1, macOS 10.14.6 (Mojave), and a retina screen

Answer 1

The first behavior seems to be a bug of v13. In v12.3.1 it works as expected:

As to the second example, this seems to be another bug introduced in v12.3.1 or earlier, because v9.0.1 works as expected:

$Version
dims = {21, 21};
pix = Image@ReplacePart[ConstantArray[0, dims], {{11, 11}} -> 1];
mask = Rasterize[Graphics[{Disk[dims/2, 6]},PlotRange -> Transpose[{{0, 0}, dims}]
    (*,ImageSize -> dims*), PlotRangePadding -> None], "Image", 
    ImageResolution -> 72, RasterSize -> dims];
(* mask + pix *)
ImageAdd[mask, pix]

For comparison here's v12.3.1 result:

Remark

1. I've removed the ImageSize option in Graphics and add the RasterSize option to Rasterize, otherwise the alignment will be wrong even in v9. (Yeah, once again, this seems to be a bug, in v9. )

2. I've used ImageAdd in v9 because the syntax mask + pix is introduced in v11.1.

3. I've explicitly set the second argument of Rasterize to "Image" in v9, because the default setting before v11.2 is "Graphics".