Incremental Attribute Computation and Image Manipulation Using Morphological Trees

In digital image processing, objects contain many pixels with different brightness or grey levels. We can group these pixels based on their brightness and their neighbouring pixels and hierarchically organise these grouped pixels in trees called morphological trees. Morphological trees can organise these grouped pixels according to their geometric inclusion, from bright regions to dark regions, or vice-versa. In this research, we propose incremental and differential methods to fast compute attributes that characterised these groups of pixels such as area, perimeter, number of holes, distance transform and contours. The proposed approaches exploit the hierarchical information encoded in the tree to reuse the attribute computation of a region which is hierarchical below its parent region. We can use these attributes for selecting regions of the image according to our task, for example, finding small objects using area, finding thin objects using the maximum distance value transform,
removing holes, and others.

We also have proposed using icicle plots for interactive manipulation and node selection of morphological trees of an image. We developed a software application that uses this interactive graphical representation and shape manipulation for editing images. The software has been successfully used for many image processing tasks such as watermark removal, data augmentation, image deformation and others.