Invertible Orientation Scores as an Application of Generalized Wavelet Theory,”

Abstract -Inspired by the visual system of many mammals, we consider the construction of-and reconstruction from-an orientation score of an image, via a wavelet transform corresponding to the left-regular representation of the Euclidean motion group in ‫ތ‬ 2 ( ‫ޒ‬ 2 ) and oriented wavelet ψ ∈ ‫ތ‬ 2 ( ‫ޒ‬ 2 ). Because this representation is reducible, the general wavelet reconstruction theorem does not apply. By means of reproducing kernel theory, we formulate a new and more general wavelet theory, which is applied to our specific case. As a result we can quantify the well-posedness of the reconstruction given the wavelet ψ and deal with the question of which oriented wavelet ψ is practically desirable in the sense that it both allows a stable reconstruction and a proper detection of local elongated structures. This enables image enhancement by means of left-invariant operators on orientation scores

MathVisionTools: Medical Image Analysis Prototyping

This paper describes a new international collaborative initiative for the assembly of a high level medical image analysis toolkit, based on Mathematica, to do efficient design and development of advanced computer vision algorithms for computer-aided diagnosis. Mathematica has come to a point that the combined symbolic and numeric power makes it a versatile and efficient framework for prototyping of complex algorithms.This is a first announcement, and call for interest and participation

Rapid prototyping of biomedical image analysis applications with Mathematica

We report on 2.5 years successful use of high level rapid prototyping in education and research of biomedical image analysis, using Mathematica

Edge Preserving Smoothing with Euclidean Shortening flow

Edge preserving smoothing is a locally adaptive process, where the size of the blurkernel, applied to suppress the noise, is a local function of the edge strength [2, 3]. Blurring is described by a partial differential equation, the diffusion equation. At strong edges, the 'conductivity' of the diffusion is reduced.This was first introduced into the realm of computer vision by Perona and Malik [4] in 1991. It was a huge success, as it also enhanced the remaining edges. But at strong edges, the noise remained, and there was a parameter k that had to be set. Alvarez [5] came up with an elegant solution for both issues, by proposing a new nonlinear image evolution scheme, where the local edge direction was taken into account. This solution is known as Euclidean Shortening Flow.We first give the theory and implementation of Perona & Malik nonlinear diffusion, then we focus on Euclidean shortening flow. The last section discusses an implementation on a noise ultrasound image. This paper is based on Chapter 21 of the book Front-End Vision & Multi-Scale Image Analysis (ter Haar Romeny, 2003)

Invertible orientation scores as an application of generalized wavelet theory

Inspired by the visual system of many mammals, we consider the construction of—and reconstruction from—an orientation score of an image, via a wavelet transform corresponding to the left-regular representation of the Euclidean motion group in (R2) and oriented wavelet f ¿ (R2). Because this representation is reducible, the general wavelet reconstruction theorem does not apply. By means of reproducing kernel theory, we formulate a new and more general wavelet theory, which is applied to our specific case. As a result we can quantify the well-posedness of the reconstruction given the wavelet f and deal with the question of which oriented wavelet f is practically desirable in the sense that it both allows a stable reconstruction and a proper detection of local elongated structures. This enables image enhancement by means of left-invariant operators on orientation scores

An efficient method for tensor voting using steerable filters

In many image analysis applications there is a need to extract curves in noisy images. To achieve a more robust extraction, one can exploit correlations of oriented features over a spatial context in the image. Tensor voting is an existing technique to extract features in this way. In this paper, we present a new computational scheme for tensor voting on a dense field of rank-2 tensors. Using steerable filter theory, it is possible to rewrite the tensor voting operation as a linear combination of complex-valued convolutions. This approach has computational advantages since convolutions can be implemented efficiently. We provide speed measurements to indicate the gain in speed, and illustrate the use of steerable tensor voting on medical applications