Image compression via tritree decomposition

The work presents a new method for image compression, using tritree decomposition (TT). TT was originally proposed by Wille (1992) for generation of non-structured finite element meshes for numerical solution of differential equation systems. TT decomposition is similar to quadtree decomposition (QT), which has been broadly used by image processing algorithms, mainly for segmentation and compression. However, while QT subdivides the image into progressively smaller quadratic regions, TT decomposition subdivides the image into triangular regions. The goal is to segment the image into a set of triangular homogeneous regions, where the differences among the pixel values don´t exceed a certain threshold. A tree is built to represent the decomposition. Each triangle will be a node of the tree TT. The initial triangle, that contains the whole image, is the root of the tree. The final triangles, representing the compressed image, are the leaves of the tree. Reconstruction of the image is accomplished by planar interpolation among the vertices of each triangular leaf.