Nahum Kiryati

A probabilistic Hough transform

Abstract The Hough Transform for straight line detection is considered. It is shown that if just a small subset of the edge points in the image, selected at random, is used as input for the Hough Transform, the performance is often only slightly impaired, thus the execution time can be considerably shortened. The performance of the resulting “Probabilistic Hough Transform” is analysed. The analysis is supported by experimental evidence.

Range imaging with adaptive color structured light

In range sensing with time-multiplexed structured light, there is a trade-off between accuracy, robustness and the acquisition period. In this paper a novel structured light method is described. Adaptation of the number and form of the projection patterns to the characteristics of the scene takes place as part of the acquisition process. Noise margins are matched to the actual noise level, thus reducing the number of projection patterns to the necessary minimum. Color is used for light plane labeling. The dimension of the pattern space are thus increased without raising the number of projection patterns. It is shown that the color of an impinging light plane can be identified from the image of the illuminated scene, even with colorful scenes. Identification is local and does not rely on spatial color sequences. The suggested approach has been implemented and the theoretical results are supported by experiments.

MRI inter-slice reconstruction using super-resolution

MRI reconstruction using super-resolution is presented and shown to improve spatial resolution in cases when spatially-selective RF pulses are used for localization. In 2-D multislice MRI, the resolution in the slice direction is often lower than the in-plane resolution. For certain diagnostic imaging applications, isotropic resolution is necessary but true 3-D acquisition methods are not practical. In this case, if the imaging volume is acquired two or more times, with small spatial shifts between acquisitions, combination of the data sets using an iterative super-resolution algorithm gives improved resolution and better edge definition in the slice-select direction. Resolution augmentation in MRI is important for visualization and early diagnosis. The method also improves the signal-to-noise efficiency of the data acquisition.

Depth from defocus vs. stereo: how different really are they?

Depth from Focus (DFF) and Depth from Defocus (DFD) methods are theoretically unified with the geometric triangulation principle. Fundamentally, the depth sensitivities of DFF and DFD are not different than those of stereo (or motion) based systems having the same physical dimensions. Contrary to common belief, DFD does not inherently avoid the matching (correspondence) problem. Basically, DFD and DFF do not avoid the occlusion problem any more than triangulation techniques, but they are more stable in the presence of such disruptions. The fundamental advantage of DFF and DFD methods is the two-dimensionality of the aperture, allowing more robust estimation. We analyze the effect of noise in different spatial frequencies, and derive the optimal changes of the focus settings in DFD. These results elucidate the limitations of methods based on depth of field and provide a foundation for fair performance comparison between DFF/DFD and shape from stereo (or motion) algorithms.

Skeletonization via distance maps and level sets

The medial axis transform (MAT) of a shape, better known as its skeleton, is frequently used in shape analysis and related areas. In this paper a new approach for determining the skeleton of an object is presented. The boundary is segmented at points of maximal positive curvature and a distance map from each of the segments is calculated. The skeleton is then located by applying simple rules to the zero sets of distance map differences. A framework is proposed for numerical approximation of distance maps that is consistent with the continuous case and hence does not suffer from digitization bias due to metrication errors of the implementation on the grid. Subpixel accuracy in distance map calculation is obtained by using gray-level information along the boundary of the shape in the numerical scheme. The accuracy of the resulting efficient skeletonization algorithm is demonstrated by several examples.

Separation of Transparent Layers using Focus

Consider situations where the depth at each point in the scene is multi-valued, due to the presence of a virtual image semi-reflected by a transparent surface. The semi-reflected image is linearly superimposed on the image of an object that is behind the transparent surface. A novel approach is proposed for the separation of the superimposed layers. Focusing on either of the layers yields initial separation, but crosstalk remains. The separation is enhanced by mutual blurring of the perturbing components in the images. However, this blurring requires the estimation of the defocus blur kernels. We thus propose a method for self calibration of the blur kernels, given the raw images. The kernels are sought to minimize the mutual information of the recovered layers. Autofocusing and depth estimation in the presence of semi-reflections are also considered. Experimental results are presented.

Image Deblurring in the Presence of Impulsive Noise

Consider the problem of image deblurring in the presence of impulsive noise. Standard image deconvolution methods rely on the Gaussian noise model and do not perform well with impulsive noise. The main challenge is to deblur the image, recover its discontinuities and at the same time remove the impulse noise. Median-based approaches are inadequate, because at high noise levels they induce nonlinear distortion that hampers the deblurring process. Distinguishing outliers from edge elements is difficult in current gradient-based edge-preserving restoration methods. The suggested approach integrates and extends the robust statistics, line process (half quadratic) and anisotropic diffusion points of view. We present a unified variational approach to image deblurring and impulse noise removal. The objective functional consists of a fidelity term and a regularizer. Data fidelity is quantified using the robust modified L1 norm, and elements from the Mumford-Shah functional are used for regularization. We show that the Mumford-Shah regularizer can be viewed as an extended line process. It reflects spatial organization properties of the image edges, that do not appear in the common line process or anisotropic diffusion. This allows to distinguish outliers from edges and leads to superior experimental results.

Polarization and statistical analysis of scenes containing a semireflector

We present an approach to recover scenes deteriorated by reflections off a semireflecting medium (e.g., a glass window). The method, based on imaging through a polarizer at two or more orientations, separates the reflected and transmitted scenes and determines which is which. We analyze the polarization effects, taking into account internal reflections within the medium. The scene reconstruction requires the estimation of the orientation (inclination and tilt angles) of the transparent (invisible) surface. The inclination angle is estimated by seeking the value that leads to the minimal mutual information of the estimated scenes. The limitations and the consequences of noise and angle error are discussed, including a fundamental ambiguity in the determination of the plane of incidence. Experimental results demonstrate the success of angle estimation and consequent scene separation and labeling.

Detecting symmetry in grey level images: the global optimization approach

The detection of significant local reflectional symmetry in grey level images is considered. Prior segmentation is not assumed, and it is intended that the results could be used for guiding visual attention and for providing side information to segmentation algorithms. A local measure of reflectional symmetry that transforms the symmetry detection problem to a global optimization problem is defined. Reflectional symmetry detection becomes equivalent to finding the global maximum of a complicated multimodal function parameterized by the location of the center of the supporting region, its size, and the orientation of the symmetry axis. Unlike previous approaches, time consuming exhaustive search is avoided. A global optimization algorithm for solving the problem is presented. It is related to genetic algorithms and to adaptive random search techniques. The efficiency of the suggested algorithm is experimentally demonstrated. Just one thousand evaluations of the local symmetry measure are typically needed in order to locate the dominant symmetry in natural test images.

Deblurring of Color Images Corrupted by Impulsive Noise

We consider the problem of restoring a multichannel image corrupted by blur and impulsive noise (e.g., salt-and-pepper noise). Using the variational framework, we consider the L1 fidelity term and several possible regularizers. In particular, we use generalizations of the Mumford-Shah (MS) functional to color images and Gamma-convergence approximations to unify deblurring and denoising. Experimental comparisons show that the MS stabilizer yields better results with respect to Beltrami and total variation regularizers. Color edge detection is a beneficial by-product of our methods