A kind user over at stackoverflow.com helped solve this issue:
In short, here's the solution:
hFig = figure('Name','APP',...
'Numbertitle','off',...
'Position', [0 0 screenWidth screenHeight],...
'WindowStyle','modal',...
'Color',[0.5 0.5 0.5],...
'Toolbar','none');
img = imread('someImage.png');
fpos = get(hFig,'Position')
axOffset = (fpos(3:4)-[size(img,2) size(img,1)])/2;
ha = axes('Parent',hFig,'Units','pixels',...
'Position',[axOffset size(img,2) size(img,1)]);
hImshow = imshow(img,'Parent',ha);
By first creating the figure window, then axes of proper size and position, and then displaying the image with imshow, using the axes as parent, the window resizing is avoided.
Cheers, Christian