The Algebraic Model with an Asymmetric Characteristic of Logarithmic Transformation

The construction of image processing methods based on the properties of the human visual system is an actual problem nowadays. Logarithmic Image Processing (LIP) approaches are used to solve it. These approaches are based on the application of logarithmic-type function at basic transformations. However, they weren’t adapted to local brightness characteristics. Therefore, an algebraic model that uses a logarithmic transformation with an asymmetric characteristic is proposed in this paper. It is shown that the given set with the proposed add operation form an Abelian group. This operation is proved to be commutative and associative. Zero and opposite elements for the group are found. Sliding image processing techniques, adapted to local characteristics, can be built based on the proposed algebraic model. The characteristic of logarithmic transformation is formed according to the local brightness distribution properties of the sliding window image elements. This ensures image processing efficiency.