A color image reduction based on fuzzy transforms

We present a new method for color image reduction based on the concept of fuzzy transform. Any image in a single band can be considered as a fuzzy matrix which is subdivided into submatrices called blocks. Each block is compressed with various_compression rates by means of a fuzzy transform in two variables. We compare our method with recent three algorithms due to G. Beliakov, H. Bustince and D. Paternain based on the minimizing penalty functions defined over a discrete lattice. The quality of the reduced image is measured by the Mean Square Error (MSE) and Penalty function (PEN) obtained by comparing both magnified and original images. We also point out a threshold of the compression rate beyond which the MSE follows a linear trend and the corresponding loss of information is still acceptable.