Representing the image as a surface, an inhomogeneous diffusion algorithm is developed, evolving the surface at a speed proportional to its mean curvature, reducing noise while preserving image structure. An adaptive scaling parameter increases the speed of the diffusion.

Partial differential equations (PDE's) have dominated image processing research recently (see Suri et al. [1], [2], [3], [4], [5], [6] and Haker [7]). The three main reasons for their success are: (1) their ability to transform a segmentation modeling problem into a partial differential equation framework and their ability to embed and integrate different regularizers into these models; (2) their ability to solve PDE's in the level set framework using finite difference methods; and (3) their easy extension to a higher dimensional space. This paper

We propose a method for estimating intrasurgical brain shift for image-guided surgery. This method consists of five stages: the identification of relevant anatomical surfaces within the MRI/CT volume, range-sensing of the skin and cortex in the OR, rigid registration of the skin range image with its MRI/CT homologue, non-rigid motion tracking over time of cortical range images, and lastly, interpolation of this surface displacement information over the whole brain volume via a realistically valued finite element model of the head. This papers focuses on the anatomical surface identification and cortical range surface tracking problems. The surface identification scheme implements a recent algorithm which imbeds 3D surface segmentation as the level-set of a 4D moving front. A by-product of this stage is a Euclidean distance and closest point map which is later exploited to speed up the rigid and non-rigid surface registration. The range-sensor uses both laser-based triangulation and def...

The application of Curvature Scale Space representation in shape similarity retrieval under affine transformation is addressed in this paper. The maxima of Curvature Scale Space (CSS) image have already been used to represent 2-D shapes in different applications. The representation has shown robustness under the similarity transformations. Scaling, orientation changes, translation and even noise can be easily handled by the representation and its associated matching algorithm. In this paper, we also consider shear and examine the performance of the representation under affine transformations. It is observed that the performance of the method is promising even under severe deformations caused by shear. The method is tested on a very large database of shapes and also evaluated objectively through a classified database. The performance of the method is compared with the performance of two well-known methods, namely Fourier descriptors and moment invariants. We also observe that global parameters such as eccentricity and circularity are no longer useful in an affine transform environment. 1

We introduce the homotopic alternating sequential filter as a new method for smoothing 2D and 3D objects in binary images. Unlike existing methods, our method offers a strict guarantee of topology preservation. This property is ensured by the exclusive use of homotopic transformations defined in the framework of digital topology. Smoothness is obtained by the use of morphological openings and closings by metric discs or balls of increasing radius, in the manner of an alternating sequential filter. The homotopic alternating sequential filter operates both on the object and on the background, in an equilibrated way. It takes an original image X and a control image C as input, and smoothes X “as much as possible ” while respecting the topology of X and geometrical constraints implicitly represented by C. Based on this filter, we introduce a general smoothing procedure with a single parameter which allows to control the degree of smoothing. Furthermore, the result of this procedure presents small variations in response to small variations of the parameter value. We also propose a method with no parameter for smoothing zoomed binary images in 2D or 3D while preserving topology.

Image smoothing based on anisotropic diffusion provides better performance than classical linear filtering. One difficulty is to compare and evaluate the different models proposed. Since the basic model arises from fluid mechanics, we propose to track anisotropic diffusion using an optical flow technique through a new physics based image model. Consequently to this, we propose a new choice for the conductance function which is easier to control. We demonstrate with the optical flow tracking that this function has a better behavior concerning the gradient threshold than the known conductance functions. 1

Partial Differential Equations (PDEs) have dominated image processing research recently. The three main reasons for their success are: first, their ability to transform a segmentation modeling problem into a partial differential equation framework and their ability to embed and integrate different regularizers into these models; second, their ability to solve PDEs in the level set framework using finite difference methods; and third, their easy extension to a higher dimensional space. This paper is an attempt to survey and understand the power of PDEs to incorporate into geometric deformable models for segmentation of objects in 2D and 3D in still and motion imagery. The paper first presents PDEs and their solutions applied to image diffusion. The main concentration of this paper is to demonstrate the usage of regularizers in PDEs and level set framework to achieve the image segmentation in still and motion imagery. Lastly, we cover miscellaneous applications such as: mathematical morphology, computation of missing boundaries for shape recovery and low pass filtering, all under the PDE framework. The paper concludes with the merits and the demerits of PDEs and level set-based framework for segmentation modeling. The paper presents a variety of examples covering both synthetic and real world images.

Some known models in phase separation theory (Hele-Shaw, nonlocal mean curvature motion), and their approximation by means of Cahn{Hilliard and nonlocal Allen-Cahn equations, are used to generate planar curve evolution without shrinkage, with application to shape recovery. This turns out to be a level set approach to an area preserving geometric ow in the spirit of Sapiro and Tannenbaum [37]. We discuss the theoretical validation of this method, together with the results of some numerical experiments. 1 1 Introduction Mathematical models based on planar curve evolution have recently been studied in Computer Vision with application to shape recovery and analysis as well as to image segmentation [22, 23, 24, 36, 37]. The curves represent the contours of objects in a grey level image and the idea is to use a geometric ow to reduce a given initial set of curves to a form which is more manageable for pattern recognition and interpretation. The curve evolution has to be designed ...

Adaptive filters or image enhancement techniques have repeatedly been suggested to make feature extraction more robust. Few comparative analysis exists and even the existing ones concern only the effect of the filter on the image but not its effect on a feature extraction process. In this paper we present an experimental approach for the evaluation of low-level vision system components in a system framework and use it on adaptive filters. As we are interested in the overall performance of the system the interactions between the algorithms and other parts of the system have to be understood. We design a general evaluation strategy and derive from it an algorithm to measure the results. In order to have objective and reproducible results the automatic control of the parameters of the vision system is necessary for which we present several techniques. The results show that none of the tested techniques performs better than linear filters or the Canny edge detector. 1 Introducti...

We present a general formulation for a new knowledge-based approach to anisotropic diffusion of multi-valued and multi-dimensional images, with an illustrative application for the enhancement and segmentation of cardiac magnetic resonance (MR) images. In the proposed method all available information is incorporated through a new definition of the conductance function which differs from previous approaches in two aspects. First, we model the conductance as an explicit function of time and position, and not only of the differential structure of the image data. Inherent properties of the system (such as geometrical features or non-homogeneous data sampling) can therefore be taken into account by allowing the conductance function to vary depending on the location in the spatial and temporal coordinate space. Secondly, by defining the conductance as a second-rank tensor, the non-homogeneous diffusion equation gains a truly anisotropic character which is essential to emulate and handle certain aspects of complex data systems. The method presented is suitable for image enhancement and segmentation of single- or multi-valued images.