A logic framework for active contours on multi-channel images

We propose a mathematical framework for object detection using logic operations as a structure for defining multi-channel segmentation. The model combines object information from the different channels into any logic combination. We consider active contour methods which use one initial contour that would evolve from the information given in each channel simultaneously. Specific models are derived based on the single-channel region based "active contours without edges" [IEEE Trans. Image Process. 10 (2) (2001) 266] model. Numerical experiments show that the method is able to find general intersections, unions, and complements of the regions of objects of both synthetic and realistic images.