Abstract-We present a novel formulation for B-spline snakes that can be used as a tool for fast and intuitive contour outlining. We start with a theoretical argument in favor of splines in the traditional formulation by showing that the optimal, curvature-constrained snake is a cubic spline, irrespective of the form of the external energy field. Unfortunately, such regularized snakes suffer from slow convergence speed because of a large number of control points, as well as from difficulties in determining the weight factors associated to the internal energies of the curve. We therefore propose an alternative formulation in which the intrinsic scale of the spline model is adjusted a priori; this leads to a reduction of the number of parameters to be optimized and eliminates the need for internal energies (i.e., the regularization term). In other words, we are now controlling the elasticity of the spline implicitly and rather intuitively by varying the spacing between the spline knots. The theory is embedded into a multiresolution formulation demonstrating improved stability in noisy image environments. Validation results are presented, comparing the traditional snake using internal energies and the proposed approach without internal energies, showing the similar performance of the latter. Several biomedical examples of applications are included to illustrate the versatility of the method.

Abstract-This paper deals with the use of some morphological tools for image and video coding. Mathematical morphology can be considered as a shape-oriented approach to signal processing, and some of its features make it very useful for compression. Rather than describing a coding algorithm, the purpose of this paper is to describe some morphological tools that have recently proved to be attractive for compression. Four sets of morphological transformations are presented: connected operators, the region-growing version of the watershed, the geodesic skeleton, and a morphological interpolation technique. Their implementation will be discussed, and we will show how they can be used for image and video segmentation, contour coding, and texture coding.

Attenuation correction is essential to PET imaging but often requires impractical acquisition times. Segmentation of short noisier transmission scans has been proposed as a solution. We report that a 3D morphological tool -the watershed algorithm -is well adapted for segmenting even 2-minute PET transmission images. The technique is noniterative, fast, and fully 3-D. It inherently ensures class continuity and eliminates outliers. Pre-filtering the data induced smoother class edges, showing that a multi-resolution approach could be used to deal with partial volume effect and excessive noise in the data. The algorithm was tested on 2-minute scans of a torso phantom and on a human study.