Lucas J. van Vliet

Recursive implementation of the Gaussian filter

Abstract In this paper we propose a recursive implementation of the Gaussian filter. This implementation yields an infinite impulse response filter that has six MADDs per dimension independent of the value of σ in the Gaussian kernel. In contrast to the Deriche implementation (1987), the coefficients of our recursive filter have a simple, closed-form solution for a desired value of the Gaussian σ. Our implementation is, in general, faster than (1) an implementation based upon direct convolution with samples of a Gaussian, (2) repeated convolutions with a kernel such as the uniform filter, and (3) an FFT implementation of a Gaussian filter.

Robust fusion of irregularly sampled data using adaptive normalized convolution

We present a novel algorithm for image fusion from irregularly sampled data. The method is based on the framework of normalized convolution (NC), in which the local signal is approximated through a projection onto a subspace. The use of polynomial basis functions in this paper makes NC equivalent to a local Taylor series expansion. Unlike the traditional framework, however, the window function of adaptive NC is adapted to local linear structures. This leads to more samples of the same modality being gathered for the analysis, which in turn improves signal-to-noise ratio and reduces diffusion across discontinuities. A robust signal certainty is also adapted to the sample intensities to minimize the influence of outliers. Excellent fusion capability of adaptive NC is demonstrated through an application of super-resolution image reconstruction.

A contour processing method for fast binary neighbourhood operations

Abstract In this paper new fast algorithms for erosion dilation, propagation and skeletonization are presented. The key principle of the algorithms is to process object contours. A queue is implemented to store the contours in each iteration for the next iteration. The contours can be passed from one operation to another as well. Contour filling and object labelling become available by minor modifications of the basic operations. The time complexity of the algoriths is linear with the number of contour elements to be processed. The algorithms prove to be faster than any other known algorithm.

Computed Cleansing for Virtual Colonoscopy Using a Three-Material Transition Model

Virtual colonoscopy is a non-invasive technique for the detection of polyps. Currently, a clean colon is required; as without cleansing the colonic wall cannot be segmented. Enhanced bowel preparation schemes opacify intraluminal remains to enable colon segmentation. Computed cleansing (as opposed to physical cleansing of the bowels) allows removal of tagged intraluminal remains. This paper describes a model that allows proper classification of transitions between three materials: gas, tissue and tagged intraluminal remains. The computed cleansing effectively detects and removes the remains from the data. Inspection of the ‘clean’ wall is possible using common surface visualization techniques.

Autofocusing in microscopy based on the OTF and sampling

Frank R. Boddeke, Lucas J. van Vliet, Hans Netten and Ian T. YoungPattern Recognition Group of the Faculty of Applied PhysicsDelft University of TechnologyLorentzweg 1, 2628 CJ Delft, The NetherlandsAbstractIn the literature many autofocus algorithms have been proposed and compared (Groen et al. 1985;Firestone at al. 1991; Yeo et al. 1993; Price and Gough 1994) for use in optical microscopy (brightfield and fluorescence microscopy). Most of the focus criteria measure the high frequency contents ofa recorded image as a measure of focus. In this paper we show that a focus criteria should measure thesignal power of the middle frequency, since defocusing mainly reduces the frequencies around halfthe cut-off frequency of the optical system. The filter that provides the required band–pass filteringdepends strongly on the sampling density of the camera. There are two practical combinations ofsampling density and one-dimensional digital band-pass filter:• Sampling at the Nyquist frequency and the {1,0,–1} filter;• Sampling at half the Nyquist frequency and the {1,–1} filter.The latter is to be preferred due to noise considerations and the fact that it uses four times fewersample points. Calculation speed can also be increased by further reducing the sampling densityperpendicular to the filter (on chip or in software) down to 1/8 of the Nyquist frequency. We havedesigned a three-phase autofocus algorithm that works well in fluorescence and bright fieldmicroscopy. The phases are:• Coarse, find the region near focus (step size of typically a few microns);• Fine, find a quadratic region around focus (step size around one micron);• Refine, use a quadratic fit on samples around the peak to find the in-focus position.We found that the final focus error is smaller than the mechanical reproducibility of our z-axis (50nm) for light levels down to 400 photo-electrons per pixel (sampling at the Nyquist frequency using acooled CCD camera with pixels of 6.8

Performance of optimal registration estimators

This paper derives a theoretical limit for image registration and presents an iterative estimator that achieves the limit. The variance of any parametric registration is bounded by the Cramer-Rao bound (CRB). This bound is signal-dependent and is proportional to the variance of input noise. Since most available registration techniques are biased, they are not optimal. The bias, however, can be reduced to practically zero by an iterative gradient-based estimator. In the proximity of a solution, this estimator converges to the CRB with a quadratic rate. Images can be brought close to each other, thus speedup the registration process, by a coarse-to-tne multi-scale registration. The performance of iterative registration is finally shown to significantly increase image resolution from multiple low resolution images under translational motions.

Grain size stabilisation by dispersed graphite in a high-grade quartz mylonite: an example from Naxos (Greece)

High grade quartz mylonites from Naxos, Greece, consist of alternating thin layers of pure quartz and quartz layers with 0.3– 3 vol.% finely dispersed graphite particles. Graphite-free layers are coarse grained (100 – 300 mm), show undulose extinction, subgrains, lobate grain boundaries and have a strongly developed crystallographic preferred orientation. In these layers, dislocation flow is interpreted to be the dominant deformation mechanism. In contrast, graphite-rich layers are fine-grained (30 – 70 mm), have equant quartz grain shapes and have a crystallographic preferred orientation that becomes progressively weaker with decreasing quartz grain size. Given the high temperature of deformation and the need for a c-axis fabric destroying mechanism, grain boundary sliding is interpreted to be important in these layers. Analysis shows an inverse relationship between quartz grain size and the graphite dispersion, suggesting stabilization of quartz grain size by graphite particles. Graphite particles larger than 5 mm are concentrated along quartz boundaries, suggesting that stabilisation only operates above a certain critical graphite particle size. This study shows that a dispersed second phase such as graphite in a naturally deforming rock can inhibit grain boundary migration, stabilise the grain size and enhance grain boundary sliding at the expense of dislocation flow. q 2002 Elsevier Science Ltd. All rights reserved.

A new sharpness measure based on gaussian lines and edges

We measure the sharpness of natural (complex) images using Gaussian models. We first locate lines and edges in the image. We apply Gaussian derivatives at different scales to the lines and edges. This yields a response function, to which we can fit the response function of model lines and edges. We can thus estimate the width and amplitude of the line or edge. As measure of the sharpness we propose the 5 th percentile of the sigmas or the fraction of line/edge pixels with a sigma smaller than 1.

Quantitative Assessment of Gas Cell Development During the Proofing of Dough by Magnetic Resonance Imaging and Image Analysis

Cereal Chem. 80(4):390–395 The structure of bread crumb is an important factor in consumer acceptance of bakery products. The noninvasive monitoring of the gas cell formation during the proofing of dough can aid in understanding the mechanisms governing the crumb appearance in the baked product. The development of gas cells during the proofing of dough was monitored in a noninvasive manner using magnetic resonance imaging (MRI) at 4.7-T. The acquired MRI time series were analyzed quantitatively using image analysis (IA) techniques. The effects of both kneading temperature and mechanical damage by molding were studied. When additional rheological stress was introduced during molding, a more heterogeneous (coarse) gas cell size distribution was observed, and the dough had a smaller specific volume (as measured by MRI). These characteristics were preserved in the bread crumb structure after baking. The fastdeformation during molding also resulted in an isotropic growth of the dough during proofing, whereas slow-deformation during molding resulted in anisotropic growth. This can be related to a better conservation of stress in the dough under a moderate molding operation. A higher temperature during kneading also resulted in a coarser distribution of the gas cells and a smaller MRI specific dough volume. No effect of kneading temperature on the growth anisotropy could be detected, however. This indicates that temperature has a smaller effect on the conservation of stress in the dough than molding. The current work illustrates the capability of MRI/IA for understanding and predicting the influence of food processing parameters on consumer-relevant features in a food product (bread).

The generalized Radon transform: Sampling, accuracy and memory considerations

The generalized Radon (or Hough) transform is a well-known tool for detecting parameterized shapes in an image. The Radon transform is a mapping between the image space and a parameter space. The coordinates of a point in the latter correspond to the parameters of a shape in the image. The amplitude at that point corresponds to the amount of evidence for that shape. In this paper we discuss three important aspects of the Radon transform. The first aspect is discretization. Using concepts from sampling theory we derive a set of sampling criteria for the generalized Radon transform. The second aspect is accuracy. For the specific case of the Radon transform for spheres, we examine how well the location of the maxima matches the true parameters. We derive a correction term to reduce the bias in the estimated radii. The third aspect concerns a projection-based algorithm to reduce memory requirements.