Natural Histogram Partitioning based on Invariant Multi-phase Level Set

Conventional image partitioning is commonly based on the histogram of the image. It is based on modal distribution and is generally modeled using the mixture of Gaussian distributions. This approach has couple of limitations. Firstly for the Gaussian, if large variance is used, then the partition may include more than one perceivable region. Secondly, if the two adjacent modal partitions are overlapped and are marginally discriminable, it may be difficult to partition. Thirdly, conventional histogram cannot be partitioned into predefined number of regions. This paper attempts to address all the three limitations using multi-phase level set functions. Here n-phase level set functions are used to partition an image into a maximum of 2" perception-based regions, i.e. if the number of perceivable regions is less than 2", then some of the regions are allowed to be empty.