Analytical and numerical solutions of the Schroedinger Equation which was satisfied by the propagator P(b, a) , including
all the paths contribution, are discussed. The definition of Schrödinger transform of image is first proposed. Exterior and
interior of objects are obtained from Schroedinger transforms of original image and its inverse image. Using the bruteforce
algorithm, sets of exterior and interior points are thinned. By finding pairs of exterior and interior points with the
smallest distance between them, contours of multiple objects are extracted. Some experiments with simulated and real
images are given.
To overcome the main drawbacks of global minimal for active contour models (L. D. Cohen and Ron Kimmel) that the
contour is only extracted partially for low SNR images, we present a new boundary extraction method, called maximal
probability method of boundary extraction. We extend the description of boundary extraction from the point of view of
classic mechanics to quantum mechanics, and propose a new boundary extraction approach based on maximal
probability of a moving particle from one point to another. Our method is based on finding a path of maximal
probability. The method includes four sequential parts: Explain boundary extraction from quantum mechanics; Estimate
the probability that a particle moves from a point to another; Find a path of maximal probability between two points;
Extract closed boundary from a single point by dividing the image into two small images. We show examples of our
method applied to real images to compare our method with global minimal for active contour models. The experiments
demonstrate that our method can overcome the main drawbacks of global minimal for active contour models.
We present a new boundary extraction model, called the quantum contour model. First, we discuss the well known and widely used deformable models from a point of view of classic mechanics. Then, boundary extraction is further considered as the motion of a particle described by quantum mechanics, which is in contrast to determining the minimum kernel energy associated with the boundary in an energy field of the deformable model. The principle and approach of boundary extraction based on particle motion in quantum mechanics are developed by estimating the probability that a particle moves from one point to another iteratively. Finally, experiments with simulated and real images demonstrate that the quantum-contour-based approach could extract a close boundary quickly, accurately, and robustly, with a single initial point close to the boundary of the object of interest.