Abstract-Level set methods have been widely used in image processing and computer vision. In conventional level set formulations, the level set function typically develops irregularities during its evolution, which may cause numerical errors and eventually destroy the stability of the evolution. Therefore, a numerical remedy, called reinitialization, is typically applied to periodically replace the degraded level set function with a signed distance function. However, the practice of reinitialization not only raises serious problems as when and how it should be performed, but also affects numerical accuracy in an undesirable way. This paper proposes a new variational level set formulation in which the regularity of the level set function is intrinsically maintained during the level set evolution. The level set evolution is derived as the gradient flow that minimizes an energy functional with a distance regularization term and an external energy that drives the motion of the zero level set toward desired locations. The distance regularization term is defined with a potential function such that the derived level set evolution has a unique forward-and-backward (FAB) diffusion effect, which is able to maintain a desired shape of the level set function, particularly a signed distance profile near the zero level set. This yields a new type of level set evolution called distance regularized level set evolution (DRLSE). The distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors. In contrast to complicated implementations of conventional level set formulations, a simpler and more efficient finite difference scheme can be used to implement the DRLSE formulation. DRLSE also allows the use of more general and efficient initialization of the level set function. In its numerical implementation, relatively large time steps can be used in the finite difference scheme to reduce the number of iterations, while ensuring sufficient numerical accuracy. To demonstrate the effectiveness of the DRLSE formulation, we apply it to an edge-based active contour model for image segmentation, and provide a simple narrowband implementation to greatly reduce computational cost.Index Terms-Forward and backward diffusion, image segmentation, level set method, narrowband, reinitialization.

Following B.B. Mandelbrot's fractal theory (1982), it was found that the fractal dimension could be obtained in medical images by the concept of fractional Brownian motion. An estimation concept for determination of the fractal dimension based upon the concept of fractional Brownian motion is discussed. Two applications are found: (1) classification; (2) edge enhancement and detection. For the purpose of classification, a normalized fractional Brownian motion feature vector is defined from this estimation concept. It represented the normalized average absolute intensity difference of pixel pairs on a surface of different scales. The feature vector uses relatively few data items to represent the statistical characteristics of the medial image surface and is invariant to linear intensity transformation. For edge enhancement and detection application, a transformed image is obtained by calculating the fractal dimension of each pixel over the whole medical image. The fractal dimension value of each pixel is obtained by calculating the fractal dimension of 7x7 pixel block centered on this pixel.

Abstract

The classification of 3 common breast lesions, fibroadenomas, cysts, and cancers, was achieved using computerized image analysis of tumor shape in conjunction with patient age. The process involved the digitization of 69 mammographic images using a video camera and a commercial frame grabber on a PC-based computer system. An interactive segmentation procedure identified the tumor boundary using a thresholding technique which successfully segmented 57% of the lesions. Several features were chosen based on the gross and fine shape describing properties of the tumor boundaries as seen on the radiographs. Patient age was included as a significant feature in determining whether the tumor was a cyst, fibroadenoma, or cancer and was the only patient history information available for this study. The concept of a radial length measure provided a basis from which 6 of the 7 shape describing features were chosen, the seventh being tumor circularity. The feature selection process was accomplished using linear discriminant analysis and a Euclidean distance metric determined group membership. The effectiveness of the classification scheme was tested using both the apparent and the leaving-one-out test methods. The best results using the apparent test method resulted in correctly classifying 82% of the tumors segmented using the entire feature space and the highest classification rate using the leaving-one-out test method was 69% using a subset of the feature space. The results using only the shape descriptors, and excluding patient age resulted in correctly classifying 72% using the entire feature space (except age), and 51% using a subset of the feature space.

No abstract