Image enhancement with weighted histogram equalization and heap transforms

Abstract

In this paper, the enhancement of the gray scale and color images, by using the weighted histogram equalization and also discrete signal-induced heap transforms (DsiHT), which are composed by elementary rotations or Givens transformations, is described. In weighted histogram equalization method, the well known histogram equalization method has been manipulated with polynomial weights to perform the better enhanced images in both gray scale and color images. In the DsiHT as a novel method of image enhancement, the angles of rotations are defined by a given signal, which is called the generator. Due to construction of the heap transform, the latter eliminates an additive component in the signal, which is similar to the generator, but transfers the energy of this component to a specific location, for instance the first point of the signal. This property of the DsiHT can effectively be used in enhancing different classes of images. The DsiHT transforms are fast and can be applied for signals of any length. Examples of enhancement of gray scale and color images by the DsiHT are described and compared with the known methods such as the histogram equalization and α-rooting method.