This paper proposes a mathematical model demonstrating that holes may be generated in images rotated through certain angles while for other rotation angles, no holes are generated. The hole effect is a classic problem in conventional image rotation, but the mechanism giving rise to the effect is not all obvious. For many image-rotation algorithms, researchers have asserted that such holes may be simply treated as a side effect. A number of individuals have discussed hole-free rotation algorithms, but few have effectively explained why such holes are generated. A total of eight definitions, six theorems, and related experiments are used here to explicate clearly the mechanism producing such image rotation holes. For those individuals who wish to develop new hole-free rotation algorithms, the model presented herein can play an important role as a future reference.
Proceedings of the National Science Council, Republic of China, Part A: Physical Science and Engineering 24(3), pp.186-194