Pixel-slop in Photoshop image rotation

See three small bitmaps attached: <<original.bmp>>; <<45cw.bmp>>; <<45ccw.bmp>>.
The original is a simple 21x21 pixel test pattern, black except for white pixels in the center and corners. It's appearance should be the same whether rotated 45 deg clockwise or counterclockwise, and the appearance should keep the symmetry of the original.
I used "Bilinear Interpolation". I used a gamma = 1 profile, and to be extra-safe set Edit>Assign Profile>Don't Color Manage ...
I set the background color to black in the toolbox. Thank you John Joslin.
Then I rotated the original image 45 deg clockwise and counterclockwise to make the other two files. Why to the resulting images look so different? Why are they lacking in symmetry? With the other interpolation methods too, clockwise and counterclockwise rotations give quite unlike images. A partial explanation could be that Photoshop rotates about a point not in the image center, but this doesn't explain enough. I tried 20x20 patterns which showed similar problems.
I'm mostly interested in bilinear interpolation because this is supposed to conserve the total pixel value. Each white pixel in the original has value 255, so the blob resulting from this pixel should have total value 255. Look at <<45cw.bmp>>.The blob on the left has total value 69+94+13+5+18+1=200. The blob on the right is an almost perfect antipode with total value 1+18+6+13+95+68=201. The blob at the bottom doesn't resemble the side blobs and has total value 42+56+40+3+55=196. The blob at the top has total value 40+41+56=137. Clearly Photoshop has lost the top of the top blob. (It also does this with 45 deg counterclockwise rotation, and also with 135 deg rotation.) The blob in the center has total value 49+49+48+47=193. All of the blobs fall far short of 255. Photoshop might be excused for messing up edge pixels, but not a central pixel.
Photoshop messes up rotation at the single pixel level. I made a test pattern with clusters of 4 white pixels and the rotation of this did conserve the total value for the central four. Edge pixels still showed problems. Photoshop image rotation appears to be based on sloppy code.

Then how do you account for my post 11? How to you account for X2 detecting a extra hidden row on the left and top side of of the image? There is no hidden row on the bottom or rightside.
Adobe digimarc did not detect anything.
Paint Shiop Pro X2 digimarc did.
I have posted the proof. It is not my fault that Adobe digimarc addon cannot detect the watermark.
The watermark is there.
dcouzin wrote:
Fantasy watermark. First of all a black pixel isn't a watermark. It can't "hide" a watermark. Hiding has no meaning in this context. If the file header has a digital ID that's fine, but it's not "hidden" in the image, not under a black pixel.
All of your reported O=255 data is not in the image either. There aren't enough bytes in the file to specify opacity at each pixel. This is a 24-bit RGB image not a 32-bit RGBO image. Maybe O=255 is specified globally somewhere in the header, but I don't see "FF" anywhere in the header. More likely full opacity is presumed for a RGB image.
THERE IS NO WATERMARK.
I suggest you download BinViewer 2.0 and BinEditor 2.0 which are freeware. Look at the file <<original.bmp>>. You will count 114 zeros between the first "FF FF FF" and the next "FF FF FF". 114 divided by 3 equals 38 so "00 00 00" appears 19 times between the "FF FF FF"s. Hey, that's the 19 black pixels between two of the corner white pixels. Now you can use BinEditor 2.0 to change some of the "0"s or "F"s to anything you want. You can write "dec9" in there. Save and open in Photoshop to see what you've painted. It's great fun creating colors and shapes by poking numbers into a file. It's the opposite of Photoshop's glistening gliding paintbrushes, and it has a powerful truth.
This is why I want to know what Photoshop does when, for example, it rotates an image.

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An aggressive, demanding, accusatory or abusive sounding post will often evoke an aggressive or abusive and unhelpful reply.
Remember, you are not addressing Adobe here in the user forums. You are requesting help from volunteers users just like you who give their time free of charge. No one has any obligation to answer your questions.
We are not here to defend Adobe or to debate users. We can only provide answers, solutions and workarounds.

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Charles:
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Pixel-slop in Photoshop image rotation

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