Ravikanth Malladi

A general framework for low level vision

We introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented. We consider intensity images as surfaces in the (x, I) space. The image is, thereby, a two-dimensional (2-D) surface in three-dimensional (3-D) space for gray-level images, and 2-D surfaces in five dimensions for color images. The new formulation unifies many classical schemes and algorithms via a simple scaling of the intensity contrast, and results in new and efficient schemes. Extensions to multidimensional signals become natural and lead to powerful denoising and scale space algorithms.

A unified approach to noise removal, image enhancement, and shape recovery

We present a unified approach to noise removal, image enhancement, and shape recovery in images. The underlying approach relies on the level set formulation of the curve and surface motion, which leads to a class of PDE-based algorithms. Beginning with an image, the first stage of this approach removes noise and enhances the image by evolving the image under flow controlled by min/max curvature and by the mean curvature. This stage is applicable to both salt-and-pepper grey-scale noise and full-image continuous noise present in black and white images, grey-scale images, texture images, and color images. The noise removal/enhancement schemes applied in this stage contain only one enhancement parameter, which in most cases is automatically chosen. The other key advantage of our approach is that a stopping criteria is automatically picked from the image; continued application of the scheme produces no further change. The second stage of our approach is the shape recovery of a desired object; we again exploit the level set approach to evolve an initial curve/surface toward the desired boundary, driven by an image-dependent speed function that automatically stops at the desired boundary.

A fast level set based algorithm for topology-independent shape modeling

Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which retains some of the attractive features of existing methods, and overcomes some of their limitations. Our technique can be applied to model arbitrarily complex shapes, which include shapes with significant protrusions, and to situations where no a priori assumption about the objects topology is made. A single instance of our model, when presented with an image having more than one object of interest, has the ability to split freely to represent each object. This method is based on the ideas developed by Osher and Sethian to model propagating solid/liquid interfaces with curvature-dependent speeds. The interface (front) is a closed, nonintersecting, hypersurface flowing along its gradient field with constant speed or a speed that depends on the curvature. It is moved by solving a “Hamilton-Jacobi” type equation written for a function in which the interface is a particular level set. A speed term synthesized from the image is used to stop the interface in the vicinity of object boundaries. The resulting equation of motion is solved by employing entropy-satisfying upwind finite difference schemes. We also introduce a new algorithm for rapid advancement of the front using what we call a narrow-band update scheme. The efficacy of the scheme is demonstrated with numerical experiments on low contrast medical images.

Constructing intrinsic parameters with active models for invariant surface reconstruction

A technique for constructing a canonical surface parameterization in terms of lines of curvature is presented. Two methods of computing the canonical invariant representation are also presented. In the first method, a static instance of the controlled continuity spline is used for the stabilizer. Ways to modify it to reflect a change of parameters to the lines of curvature are described. In the second method, the dynamic instance of the controlled continuity spline called the deformable model is used. A force field defined in terms of the principal vectors is synthesized and applied to the parameter curves of the deformable model to coerce them along the lines of curvature. In essence, any transformation of parameters requires a modification of the stabilizer in the first method, whereas in the second method, it is tantamount to synthesizing a new force field. Experimental results with real and synthetic range data are included. >

A unified geometric model for 3D confocal image analysis in cytology

In this paper, we use partial differential equation based analysis as a methodology for computer-aided cytology. We wish to accurately extract and classify the shapes of nuclei from noisy confocal microscopy images. This is a prerequisite to an accurate quantitative intranuclear (genotypic and phenotypic) and internuclear (tissue structure) analysis of cancerous and pre-cancerous specimens. We study the use of a geometric-driven scheme for improving the results obtained by a nuclear segmentation method, based on automatic segmentation, followed by object reconstruction and interactive classification. We build a chain of methods that includes an edge-preserving image smoothing mechanism, an automatic (albeit non-regularized) segmentation method, a geometry-driven scheme to regularize the shapes and improve edge fidelity, and an interactive method to split shape clusters and reclassify them.

Fast Methods for Shape Extraction in Medical and Biomedical Imaging

We present a fast shape recovery technique in 2D and 3D with specific applications in modeling shapes from medical and biomedical imagery. This approach and the algorithms described is similar in spirit to our previous work in [16,18], is topologically adaptable, and runs in O(N log N) time where N is the total number of points visited in the domain. Our technique is based on the level set shape recovery scheme introduced in [16,3] and the fast marching method in [27] for computing solutions to static Hamilton-Jacobi equations.

Intrinsic parameters for surface representation using deformable models

A canonical intrinsic parameterization that provides a consistent, invariant form for describing surfaces is defined and constructed using an elastically deformable model. The salient features of this method are that it provides a unified and general framework for reparameterization of a surface and easily allows for incorporation of multiview data sets. The canonical parameterization of the surface is defined in terms of the surface lines of curvature. Depth constraints are first imposed as an external force field on the deformable model that molds itself to be consistent with the data. Principal vectors computed from this conformed model surface are then imposed as a force field on the parameter curves of the model. The parameter curves deform to become tangential to the principal vectors thereby yielding an invariant surface parameterized by the lines of curvature. Extension of the canonical parametric grid to multiple views is demonstrated by incorporating depth and curvature constraints from multiple views. >

Image smoothing and enhancement via min/max curvature flow

We present a class of PDE-based algorithms suitable for a wide range of image processing applications. The techniques are applicable to both salt-and-pepper gray-scale noise and full- image continuous noise present in black and white images, gray-scale images, texture images and color images. At the core, the techniques rely on a level set formulation of evolving curves and surfaces and the viscosity in profile evolution. Essentially, the method consists of moving the isointensity contours in an image under curvature dependent speed laws to achieve enhancement. Compared to existing techniques, our approach has several distinct advantages. First, it contains only one enhancement parameter, which in most cases is automatically chosen. Second, the scheme automatically stops smoothing at some optimal point; continued application of the scheme produces no further change. Third, the method is one of the fastest possible schemes based on a curvature-controlled approach.