Publications by Mathews Jacob | EPFL Graph Search

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We analyze the representation of periodic signals in a scaling function basis. This representation is sufficiently general to include the widely used approximation schemes like wavelets, splines and Fourier series representation. We derive a closed form expression for the approximation error in the scaling function representation. The error formula takes the simple form of a Parseval like sum, weighted by an appropriate error kernel. This formula may be useful in choosing the right representation for a clas

We present a method for the exact computation of the moments of a region bounded by a curve represented by a scaling function or wavelet basis. Using Green's Theorem, we show that the computation of the area moments is equivalent to applying a suitable multidimensional filter on the coefficients of the curve and thereafter computing a scalar product. The multidimensional filter coefficients are precomputed exactly as the solution of a two-scale relation. To demonstrate the performance improvement of the new

We present an exact algorithm for the computation of the moments of a region bounded by a curve represented in a scaling function or wavelet basis. Using Green's theorem, we show that the computation of the area moments is equivalent to applying a suitable multidimensional filter on the coefficients of the curve and thereafter computing a scalar product. We compare this algorithm with existing methods such as pixel-based approaches and approximation of the region by a polygon.

Parametric active contour models are one of the preferred approaches for image segmentation because of their computational efficiency and simplicity. However, they have a few drawbacks which limit their performance. In this paper, we identify some of these problems and propose efficient solutions to get around them. The widely-used gradient magnitude-based energy is parameter dependent; its use will negatively affect the parametrization of the curve and, consequently, its stiffness. Hence, we introduce a ne

We present a new family of 2D orthogonal wavelets which uses quincunx sampling. The orthogonal refinement filters have a simple analytical expression in the Fourier domain as a function of the order α, which may be non-integer. The wavelets have good isotropy properties. We can also prove that they yield wavelet bases of

L _{ 2 }

(\Re ^{ 2 }

) for any α > 0. The wavelets are fractional in the sense that the approximation error at a given scale a decays like

O(a ^{ \alpha }

); they also essential

We propose an algorithm for the 3-D reconstruction of DNA filaments from a pair of stereo cryo-electron micrographs. The underlying principle is to specify a 3-D model of a filament—described as a spline curve—and to fit it to the 2-D data using a snake-like algorithm. To drive the snake, we constructed a ridge-enhancing vector field for each of the images based on the maximum output of a bank of rotating matched filters. The magnitude of the field gives a confidence measure for the presence of a filament a

We introduce a 3-D parametric active contour algorithm for the shape estimation of DNA molecules from stereo cryo-electron micrographs. We consider a 3-D filament (consisting of a B-spline skeleton and a specified radial profile) and match its projections with the micrographs using an optimization algorithm. To accelerate the evaluation of the projections, we approximate the global model locally by an elongated blob-like template that is designed to be projection-steerable. This means that the 2-D projectio

We present an exact expression for the

L _{ 2 }

error that occurs when one approximates a periodic signal in a basis of shifted and scaled versions of a generating function. This formulation is applicable to a wide variety of linear approximation schemes including wavelets, splines, and bandlimited signal expansions. The formula takes the simple form of a Parseval's-like relation, where the Fourier coefficients of the signal are weighted against a frequency kernel that characterizes the approximation op

In this paper, we present different solutions for improving spline-based snakes. First, we demonstrate their minimum curvature interpolation property, and use it as an argument to get rid of the explicit smoothness constraint. We also propose a new external energy obtained by integrating a non-linearly pre-processed image in the closed region bounded by the curve. We show that this energy, besides being efficiently computable, is sufficiently general to include the widely used gradient-based schemes, Bayesi

To assist neurobiologists investigating the molecular mechanisms involved in neurite formation and differentiation, we have developed an interactive technique for the tracing and quantification of elongated image structures. The technique is based on an improved steerable filter for computing local ridge strength and orientation. It also uses a graph-searching algorithm with a novel cost function exploiting these image features to obtain globally optimal tracings between user-defined control points. To comp

Background: For the investigation of the molecular mechanisms involved in neurite outgrowth and differentiation, accurate and reproducible segmentation and quantification of neuronal processes are a prerequisite. To facilitate this task, we developed a semiautomatic neurite tracing technique. This article describes the design and validation of the technique. Methods: The technique was compared to fully manual delineation. Four observers repeatedly traced selected neurites in 20 fluorescence microscopy image

Magnetic resonance spectroscopy imaging (MRSI) is a promising and developing tool in medical imaging. Because of various difficulties imposed by the imperfections of the scanner and the reconstruction algorithms, its applicability in clinical practice is r ...

We propose a general approach for the design of 2D feature detectors from a class of steerable functions based on the optimization of a Canny-like criterion. In contrast with previous computational designs, our approach is truly 2D and provides filters that have closed-form expressions. It also yields operators that have a better orientation selectivity than the classical gradient or Hessian-based detectors. We illustrate the method with the design of operators for edge and ridge detection. We present some

Magnetic resonance spectroscopy imaging (MRSI) is an attractive tool for medical imaging. However, its practical use is often limited by the intrinsic low spatial resolution and long acquisition time. Spectral localization by imaging (SLIM) has been propos ...

We introduce a three-dimensional (3-D) parametric active contour algorithm for the shape estimation of DNA molecules from stereo cryo-electron micrographs. We estimate the shape by matching the projections of a 3-D global shape model with the micrographs; ...

We present a new approach for the design of optimal steerable 2-D templates for feature detection. As opposed to classical schemes where the optimal 1-D template is derived and extended to 2-D, we directly obtain the 2-D template. We choose the template from a class of steerable functions based on the analytic optimization of a Canny-like criterion. Our approach gives more orientation selective templates that have simple closed form expression. We illustrate the method with the design of operators for edge

In this thesis, we present a coherent and consistent approach for the estimation of shape and shape attributes from noisy images. As compared to the traditional sequential approach, our scheme is centered on a shape model which drives the feature extraction, shape optimization, and the attribute evaluation modules. In the first section, we deal with the detection of image features that guide the shape-extraction process. We propose a general approach for the design of 2-D feature detectors from a class of s

In this paper we propose a new, interactive technique for the segmentation of elongated structures in images. It is based on the so-called live-wire segmentation paradigm and uses a newly developed steerable filter for computing local ridge strength and orientation. We describe the principles of our segmentation technique and present the results of preliminary experiments demonstrating its potential for the tracing of neurites in fluorescence microscopy images.

We use cryo-electron microscopy to compare 3D shapes of 158 bp long DNA minicircles that differ only in the sequence within an 18 bp block containing either a TATA box or a catabolite activator protein binding site. We present a sorting algorithm that corr ...

We present a framework for feature detection in 3-D using steerable filters. These filters can be designed to optimally respond to a particular type of feature by maximizing several Canny-like criteria. The detection process involves the analytical computa ...

Mathews Jacob

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An Error Analysis for the Sampling of Periodic Signals

An Exact Method for Computing the Area Moments of Wavelet and Spline Curves

Exact Computation of Area Moments for Spline and Wavelet Curves

Efficient Energies and Algorithms for Parametric Snakes

Orthogonal Quincunx Wavelets with Fractional Orders

3-D Reconstruction of DNA Filaments from Stereo Cryo-Electron Micrographs

Shape Estimation of 3-D DNA Molecules from Stereo Cryo-Electron Micro-Graphs

Sampling of Periodic Signals: A Quantitative Error Analysis

A Unifying Approach and Interface for Spline-Based Snakes

Neurite Tracing in Fluorescence Microscopy Images Using Ridge Filtering and Graph Searching: Principles and Validation

Design and Validation of a Tool for Neurite Tracing and Analysis in Fluorescence Microscopy Images

Improved MRSI with Field Inhomogeneity Compensation

Design of Steerable Filters for Feature Detection Using Canny-Like Criteria

BSLIM: Spectral Localization by Imaging with Explicit $ B _{ 0 } $ Field Inhomogeneity Compensation

3-D Shape Estimation of DNA Molecules from Stereo Cryo-Electron Micro-Graphs Using a Projection-Steerable Snake

Optimal Steerable Filters for Feature Detection

Parametric shape processing in biomedical imaging

A Novel Approach to Neurite Tracing in Fluorescence Microscopy Images

3D Reconstruction and Comparison of Shapes of DNA Minicircles Observed by Cryo-Electron Microscopy

Three-Dimensional Feature Detection Using Optimal Steerable Filters