Image transformation has two important functions. One is to produce a variety of image samples from a given image. Another is to convert a given image into one which can be processed more easily or with a better result. An example of this is image normalization. In this paper, several theorems on image transformations have been proved and new algorithms has been proposed to perform the functions mentioned above. These algorithms perform the mapping and filling at the same time while respecting the connectivity of the original image. As a result, the transformations become more consistent and accurate. The essential parallelism in the new algorithms also facilitates their implementation using VLSI architecture such that the time complexity is only O(N) compared with O(N) using a uniprocessor, where N is the dimension of the image plane. The new algorithms can handle all kinds of images including those of long narrow objects which present problems to other algorithms. They also reduce the errors introduced by the order in which rotation and scaling are applied. A series of experiments have also been conducted to verify the performance of the proposed algorithms. The results indicate that the new algorithms and VLSI architectures can be very useful to image processing, pattern recognition and related areas, especially real-time applications. © 1990.