Structure preserving binary image morphing using Delaunay triangulation

Abstract

Mathematical morphology has been of a great significance to several scientific fields. Dilation, as one of the fundamental operations, has been very much reliant on the common methods based on the set theory and on using specific shaped structuring elements to morph binary blobs. We hypothesised that by performing morphological dilation while exploiting geometry relationship between dot patterns, one can gain some advantages. The Delaunay triangulation was our choice to examine the feasibility of such hypothesis due to its favourable geometric properties. We compared our proposed algorithm to existing methods and it becomes apparent that Delaunay based dilation has the potential to emerge as a powerful tool in preserving objects structure and elucidating the influence of noise. Additionally, defining a structuring element is no longer needed in the proposed method and the dilation is adaptive to the topology of the dot patterns. We assessed the property of object structure preservation by using common measurement metrics. We also demonstrated such property through handwritten digit classification using HOG descriptors extracted from dilated images of different approaches and trained using Support Vector Machines. The confusion matrix shows that our algorithm has the best accuracy estimate in 80% of the cases. In both experiments, our approach shows a consistent improved performance over other methods which advocates for the suitability of the proposed method.