Output details

An extension of min/max flow framework

Originality: Digital images occupy an important part of our daily life. Inevitably they are contaminated by noise in the process of acquisition, storage and transmission, which can make objects recognition difficult. Consequently features or regions of interest within images may need to be enhanced to aid object recognition. This work is a continuation of our previous research (H. Yu et al. “GVF-based anisotropic diffusion models”, IEEE Trans. on Image Process., 15(6):1517-24, 2006) that introduces the Gradient Vector Flow (GVF) fields into image restoration for improving the numerical stability of the partial differential equation (PDE) based models. In this work, we introduced the GVF fields into the computation of the well-known min/max flow scheme. Besides improving the numerical stability, this also speeds up the convergence of the computation model.

Rigour: With mathematical proofs and numerical experiments, our research demonstrated a clear advantage over the existing technology. In particular, we demonstrate that the original min/max flow scheme has three drawbacks: (1) multiple iterations will result in the speckle points; (2) the curvature flow cannot adaptively stop; and (3) the boundary leaking problem. By incorporating this technique with GVF fields, our new development successfully overcomes these deficiencies.

Significance: This work sets a theoretical foundation for PDE-based image restoration. One of the main deficiencies of existing methods is that they are numerically unstable, and are both time-consuming and sensitive to noise. Our work does not only overcome the numerical difficulties of the original min/max flow scheme, but also extend it to object tracking, which is a useful operation often used in compositing live imagery with animation.