Image Reduction Operators as Aggregation Functions: Fuzzy Transform and Undersampling

After studying several reduction algorithms that can be found in the literature, we notice that there is not an axiomatic definition of this concept. In this work we propose the definition of weak reduction operators and we propose the properties of the original image that reduced images must keep. From this definition, we study whether two methods of image reduction, under sampling and fuzzy transform, satisfy the conditions of weak reduction operators.