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Not exactly sure what you want, and not sure if what you think you want is really what you need. If you have the mask, then regionprops() automatically ignores the black pixels while making measurements. So matching, segmenting, and extracting (as you asked for) are NOT needed.
You cannot get rid of black pixels because an image has to remain rectangular. However, if you want to extract only the white pixels into a list (a 1-D vector) you can pass the mask in to the gray scale image as an index:
selectedPixelValues = grayImage(mask); % Vector of only gray levels within mask
If you want a masked image where the white parts show up in their original gray scale and the background is black, you can create a masked image like this:
% Mask the image using bsxfun() function to multiply the mask by each channel individually. Works for gray scale as well as RGB Color images.
maskedRgbImage = bsxfun(@times, rgbImage, cast(mask, 'like', rgbImage));
If you want to crop off some of the black, to make a smaller image, you could, but it's not really necessary.
[r, c] = find(mask);
croppedImage = grayImage(min(r):max(r), min(c):max(c), :);
