Extract Object Boundaries in Noisy Images Quming Zhou

Sample Images

Level Set An implicit form of a closed curve: By the chain rule, The movement equation of a close curve: with

Edge Map Edge Map points toward the closet boundary pixel with its magnitude represent the total gradient energy in the half plane. The local edge vector at pixel s along the orientation θ is given as The edge map for pixel s is defined by

The Integration Range The intensity difference between pixel and pixel is To quantify the prediction of the boundary , an index is defined as The maximize the integration of in the corresponding half plane as

Edge Map The direction of the edge map points to its nearest boundary as its magnitude varies with the distance from the boundary.

Speed Function A scaling function of the edge map is given as where is the angle between the edge map and the outward normal vector of the curve. The speed function in the outward normal direction of the curve is where c and ε are constants, k is the curvature.

Narrow Band Level Set The total computational complexity 2D image domain is Narrow band is , where m is the number of pixels in the narrow band.

Example I

Example II

Example III

Conclusion The proposed approach uses both the edge direction and the gradient magnitude to overcome the problems resulting from weak edges. The results are significantly superior than results obtained using edge magnitude alone.