Improved adjoin-list for quality-guided phase unwrapping based on red-black trees

Abstract

The quality-guide phase unwrapping is an important technique that is based on quality maps which guide the unwrapping process. The efficiency of this technique depends in the adjoin-list data structure implementation. There exists several proposals that improve the adjoin-list; Ming Zhao et. al. proposed an Indexed Interwoven Linked List (I2L2) that is based on dividing the quality values into intervals of equal size and inserting in a linked list those pixels with quality values within a certain interval. Ming Zhao and Qian Kemao proposed an improved I2L2 replacing each linked list in each interval by a heap data structure, which allows efficient procedures for insertion and deletion. In this paper, we propose an improved I2L2 which uses Red-Black trees (RBT) data structures for each interval. Our proposal has as main goal to avoid the unbalanced properties of the head and thus, reducing the time complexity of insertion. In order to maintain the same efficiency of the heap when deleting an element, we provide an efficient way to remove the pixel with the highest quality value in the RBT using a pointer to the rightmost element in the tree. We also provide a new partition strategy of the phase values that is based on a density criterion. Experimental results applied to phase shifting profilometry are shown for large images.