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.

Quadtree-like pyramids have the advantage of re-suiting in a multiresolution representation where each pyramid node has four unambiguous parents. Such a centered topology guarantees a clearly defined up-projection of labels. This concept has been successfully and extensively used in applications of contour detection, object recognition and segmentation. Unfortunately, the quadtree-like type of pyramid has poor approximation powers because of the employed piecewise-constant image model. This paper deals with the construction of improved centered image pyramids in terms of general approximation functions. The advantages of the centered topology such a symmetry, consistent boundary conditions and accurate up-projection of labels are combined with a more faithful image representation at coarser pyramid levels. We start by introducing a general framework for the design of least squares pyramids using the standard filtering and decimation tools. We give the most general explicit formulas for the computation of the filter coefficients by any (well behaving) approximation function in both the continuous (L(2)) and the discrete (l(2)) norm. We then define centered pyramids and provide the filter coefficients for odd spline approximation functions. Finally, we compare the centered pyramid to the ordinary one and highlight some applications.

We present a novel formulation for B-spline snakes that can be used as a tool for fast and intuitive contour outlining. The theory is implemented in a platform independent JAVA interface, which allows real time computation of the snake curve. In this paper, our main focus is on two points. First, we propose a novel B-spline snake formulation, where the intrinsic scale of the spline model is adjusted a priori. It leads to a reduction of the number of parameters to be optimized and eliminates the need for internal energies. The approach solves the two main drawbacks of traditional snakes (slow convergence speed and difficult to adjust weighting factors for internal energy terms). Second, we comment on our experience using JAVA for the implementation of the snake and for the design of the graphical user interface. Our technique provides a very intuitive, user-friendly, and platform independent tool for contour outlining, generally applicable to a vast range of images. Several biomedical examples of applications are included to illustrate the versatility of the method.

Describes an image processing system for the automatic assessment of ejection fraction (EF) from noisy SPECT left ventricular myocardial perfusion images. A segmentation scheme consisting of an elliptical coordinate transformation, matched filtering and dynamic contour tracking detects the endo- and epicardial boundaries. Computation of EF is performed based on the epi- rather than the endocardial boundary, which proves to be more robust for images with low signal-to-noise ratios. The computation incorporates anatomical constraints of constant myocardial mass and smooth cardiac variation. The algorithm was tested on different image modalities and shows good linear agreement with EFs obtained from conventional approaches based on planar gated blood pool imaging (PET: y=8.7+1.07x, r=0.84, Technetium-99m MIBI SPECT: y=5.0+0.80x, r=0.90, Thallium-201 SPECT: y=23.5+0.82x, r=0.77, RMS error=10.0). The proposed scheme may be an alternative for EF computation without the need for additional image acquisitions.

This paper deals with the use of some morphological tools for video coding at very low bit rates. Rather than describing a complete coding algorithm, the purpose of this paper is to focus on morphological connected operators and segmentation tools that have proved to be attractive for compression.

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 proved 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. The authors discuss their implementation, and show how they can be used for image and video segmentation, contour coding, and texture coding.

Shape representation is an important image analysis task which can be used for contour coding and feature extraction. The morphological skeleton is a geometrical shape description by means of maximal inscribed structuring elements. The form of the structuring element is usually chosen a priori, and we show how genetic algorithms can be used for an automatic optimization of an arbitrary shaped structuring element. It permits improved progressive contour transmission and the extraction of shape features.

Region based coding schemes are among the most promising compression techniques for very low bit-rates. They consist of image segmentation, contour and texture coding. In this paper, a new shape representation for segmented images based on the geodesic morphological skeleton is presented. It is used for the coding of contour prediction residues obtained after motion compensation based on temporally modeled motion vectors. A non-reversible pre-skeletonization filter removes contour noise. A reversible post-skeletonization filter allows progressive transmission of contour information. It is based on the spatial distribution of the skeleton points, which are found to be close to known contours.>

This paper presents a hierarchical motion estimation method considering both a large spatial and temporal support. The problem of motion estimation is formulated as a time-varying parameter estimation problem. The main advantage of the proposed algorithm is its ability to constrain the computation of the flow field spatially and temporally at the same time, by defining each motion parameter as a linear combination of some orthogonal time functions. The number of time basis varies according to the complexity of the movement and is determined automatically by means of a multiresolution approach and of statistical tests. We also present two different applications which underline the validity of the chosen approach.