Publications/xu.15.prl.inc

Materials

Mumford-Shah Simplification on the color tree of shapes

You can download the x86_64 binary to compute the Mumford-Shah simplification running on the color tree of shapes Here.

Usage: ./mumford_shah_on_ctos input[rgb] α₀ α₁ λ output[rgb]
α₀	Grain filter size before merging trees (0 to disable)
α₁	Grain filter size on the color ToS (0 to disable)
λ	Mumford-shah regularisation weight (e.g. 5000)

Input RGB Image
Output Simplified Image

Multivariate Tree of Shapes Computation Binaries

You can download the x86_64 binaries to compute the Multivariate Tree of Shapes Here. This application outputs 16-bits image where each pixel stores the depth of the node it belongs to. To recover the MToS from this image, one just has to compute its max-tree. Note that the image is twice has big has the original one and has a border for topogical and algorithmic purposes. Thus, any pixel with coordinates (x,y) in the original image is now at coordinates (2*(x+1), 2*(y+1)) in the depth image. The application also outputs a 8bits grayscale version of the depth image that can be used to vizualise the shapes by thresholding this image.

Usage: ./compute_ctos-demo [options] input depth16.tiff depth8.png

Input RGB Image
8-bit depth Image

Illustrations

Natural image simplification with the Mumford-Shah functional optimized on the MToS

The method minimizes the Mumford-Shah cartoon model constrained by the tree topology. It removes nodes from the tree until the energy doest not decrease anymore. The tests were performed on the Weizmann database. Some samples are given below and full results are available in this archive.