Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which requires e.g. that a brightness constancy assumption holds, and a regularizer that encourages global or piecewise smoothness of the flow field. In this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images. This taxonomy provides a unifying framework for data-driven and flow-driven, isotropic and anisotropic, as well as spatial and spatio-temporal regularizers. While some of these techniques are classic methods from the literature, others are derived here for the first time. We prove that all these methods are well-posed: they posses a unique solution that depends in a continuous way on the initial data. An interesting structural relation between isotropic and anisotropic flow-driven regularizers is identified, and a design criterion is proposed for constructing anisotropic flow-driven regularizers in a simple and direct way from isotropic ones. Its use is illustrated by several examples.

In this paper we introduce a new method for image smoothing based on a fourth order PDE model. The method is tested on a broad range of medical magnetic resonance images, both in space and time, as well as on non-medical test images. Our algorithm demonstrates good noise suppression with preservation of edges and contours and without destruction of important anatomical or functional detail, even at poor signal-to-noise ratios. We have also compared our method with a related second-order PDE model and nd our method to perform overall better on the images being tested.

The goal of this paper is to present a unified description of diffusion and regularization techniques for vector-valued as well as matrix-valued data fields. In the vector-valued setting, we first review a number of existing methods and classify them into linear and nonlinear as well as isotropic and anisotropic methods. For these approaches we present corresponding regularization methods. This taxonomy is applied to the design of regularization methods for variational motion analysis in image sequences. Our vector-valued framework is then extended to the smoothing of positive semidefinite matrix fields. In this context a novel class of anisotropic di usion and regularization methods is derived and it is shown that suitable algorithmic realizations preserve the positive semidefiniteness of the matrix field without any additional constraints. As an application, we present an anisotropic nonlinear structure tensor and illustrate its advantages over the linear structure tensor.

In this paper, we introduce an image processing operator called Image Foresting Transformation (IFT ). The image foresting transformation maps an input image into a graph, computes a shortest-path forest in this graph, and outputs an annotated image, which is basically an image and its associated forest. We describe the application of IFT to region growing, edge detection, Euclidean distance transform, geodesic distance computation, and watershed transformation. All the operators are eciently computed using the same IFT algorithm based on the same set of parameters by changing only their meaning and values. We also present a new interactive image segmentation paradigm based on the region growing operator and discuss other applications of the IFT for boundary-based object denition and shape-based interpolation. 1 Introduction The use of graph in computer vision and image processing has been investigated for many years now. Its motivation stems from a solid theory with many e...

A fully automatic procedure for brain tissue classification from 3D magnetic resonance head images (MRI) is described. The procedure uses feature space proximity measures, and does not make any assumptions about the tissue intensity data distributions. As opposed to existing methods for automatic tissue classification, which are often sensitive to anatomical variability and pathology, the proposed procedure is robust against morphological deviations from the model. A novel method for automatic generation of classifier training samples, using a minimum spanning tree graph-theoretic approach, is proposed in this thesis. Starting from a set of samples generated from prior tissue probability maps (the ``model'') in a standard, brain-based coordinate system (``stereotaxic space''), the method reduces the fraction of incorrectly labelled samples in this set from 25\% down to 2\%. The corrected set of samples is then used by a supervised classifier for classifying the entire 3D image. Validation experiments were performed on both real and simulated MRI data; the kappa similarity measure increased from 0.90 to 0.95.

Medical imaging often requires a preprocessing step where filters are applied that remove noise while preserving semantically important structures such as edges. This may help to simplify subsequent tasks such as segmentation. One dass of recent adaptive denoising methods consists of methods based on nonlinear partial differential equations (PDEs). In the present paper we survey our recent results on PDE-based preprocessing methods that may be applied to medical imaging problems. We focus on nonlinear diffusion filters and variational restoration methods. We explain the basic ideas, sketch some algorithmic aspects, illustrate the concepts by applying them to medical images such as mammograms, computerized tomography (CT), and magnetic resonance (MR) images. In particular we show the use of these filters as preprocessing steps for segmentation algorithms. 1

We propose a computational algorithm for incorporating total variational (TV) regularization in positron emission tomography (PET). The motivation for using TV is that it has been shown to suppress noise effectively while capturing sharp edges without oscillations. This feature makes it particularly attractive for those applications of PET where the objective is to identify the shape of objects (e.g. tumors) that are distinguished from the background by sharp edges. We show that the standard EM algorithm can be modi ed to incorporate the TV regularization, resulting in an algorithm that is convergent independent of the amount of regularization.