the black parts are created when the new rotated image is created, and so are part of the image. if you know the colour of your figure/GUI window background, you can just run the rotated image through a line that converts any added voxels into that colour. just substituting based on colour might affect genuine in-image voxels, so using a mask is safer.
this code runs for a figure, rather than a GUI, but shows the idea:
%% rotate image and 'hide' black fill from rotation
% read in colour image (use matlab example)
[I,cmp] = imread('corn.tif');
I = ind2rgb(I,cmp);
J = imrotate(I,35,'bilinear');
% convert black pixels from rotation to figure colour using mask
mask = ones(size(I));
maskrot = ceil(imrotate(mask,35, 'bilinear')); % same transform as image
figure; figCol = get(gcf, 'Color'); % get figure background colour (RGB)
maskColour = ~maskrot.*reshape(figCol, [1 1 3]);
K = J.*maskrot + maskColour;
% show
subplot(2,3,1); imshow(mask); title('mask is image size');
subplot(2,3,2); imshow(maskrot); title('rotated mask');
subplot(2,3,3); imshow(maskColour); title('applied background mask');
subplot(2,3,4); imshow(I); title('orig figure');
subplot(2,3,5); imshow(J); title('rotated figure');
subplot(2,3,6); imshow(K); title('applied background mask');
