Oscar Nestares

Robust multiresolution alignment of MRI brain volumes.

An algorithm for the automatic alignment of MRI volumes of the human brain was developed, based on techniques adopted from the computer vision literature for image motion estimation. Most image registration techniques rely on the assumption that corresponding voxels in the two volumes have equal intensity, which is not true for MRI volumes acquired with different coils and/or pulse sequences. Intensity normalization and contrast equalization were used to minimize the differences between the intensities of the two volumes. However, these preprocessing steps do not correct perfectly for the image differences when using different coils and/or pulse sequences. Hence, the alignment algorithm relies on robust estimation, which automatically ignores voxels where the intensities are sufficiently different in the two volumes. A multiresolution pyramid implementation enables the algorithm to estimate large displacements. The resulting algorithm is used routinely to align MRI volumes acquired using different protocols (3D SPGR and 2D fast spin echo) and different coils (surface and head) to subvoxel accuracy (better than 1 mm). Magn Reson Med 43:705–715, 2000.

Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions

Gabor schemes of multiscale image representation are useful in many computer vision applications. However, the classic Gabor expansion is computationally expensive due to the lack of orthogonality of Gabor functions. Some alternative schemes, based on the application of a bank of Gabor filters, have important advantages such as computational efficiency and robustness, at the cost of redundancy and lack of completeness. In a previous work we proposed a quasicomplete Gabor transform, suitable for fast implementations in either space or frequency domains. Reconstruction was achieved by simply adding together the even Gabor channels. We develop an optimized spatial-domain implementation, using one-dimensional 11-tap filter masks, that is faster and more flexible than Fourier implementations. The reconstruction method is improved by applying fixed and independent weights to the Gabor channels before adding them together. Finally, we analyze and implement, in the spatial domain, two ways to incorporate a high-pass residual, which permits a visually complete representation of the image.

Likelihood functions and confidence bounds for total-least-squares problems

This paper addresses the derivation of likelihood functions and confidence bounds for problems involving over-determined linear systems with noise in all measurements, often referred to as total-least-squares (TLS). It has been shown previously that TLS provides maximum likelihood estimates. But rather than being a function solely of the variables of interest, the associated likelihood functions increase in dimensionality with the number of equations. This has made it difficult to derive suitable confidence bounds, and impractical to use these probability functions with Bayesian belief propagation or Bayesian tracking. This paper derives likelihood functions that are defined only on the parameters of interest. This has two main advantages. First, the likelihood functions are much easier to use within a Bayesian framework; and second it is straightforward to obtain a reliable confidence bound on the estimates. We demonstrate the accuracy of our confidence bound in relation to others that have been proposed. Also, we use our theoretical results to obtain likelihood functions for estimating the direction of 3D camera translation.

Texture synthesis‐by‐analysis method based on a multiscale early‐vision model

A new texture synthesis-by-analysis method, applying a visu- ally based approach that has some important advantages over more traditional texture modeling and synthesis techniques is introduced. The basis of the method is to encode the textural information by sampling both the power spectrum and the histogram of homogeneously textured images. The spectrum is sampled in a log-polar grid using a pyramid Gabor scheme. The input image is split into a set of 16 Gabor channels (using four spatial frequency levels and four orientations), plus a low- pass residual (LPR). The energy and equivalent bandwidths of each channel, as well as the LPR power spectrum and the histogram, are measured and the latter two are compressed. The synthesis process consists of generating 16 Gabor filtered independent noise signals with spectral centers equal to those of the Gabor filters, whose energy and equivalent bandwidths are calculated to reproduce the measured values. These bandpass signals are mixed into a single image, whose LPR power spectrum and histogram are modified to match the original fea- tures. Despite the coarse sampling scheme used, very good results have been achieved with nonstructured textures as well as with some quasi- periodic textures. Besides being applicable to a wide range of textures, the method is robust (stable, fully automatic, linear, and with a fixed code length) and compact (it uses only 69 parameters).

Bayesian model of Snellen visual acuity.

A Bayesian model of Snellen visual acuity (VA) has been developed that, as far as we know, is the first one that includes the three main stages of VA: (1) optical degradations, (2) neural image representation and contrast thresholding, and (3) character recognition. The retinal image of a Snellen test chart is obtained from experimental wave-aberration data. Then a subband image decomposition with a set of visual channels tuned to different spatial frequencies and orientations is applied to the retinal image, as in standard computational models of early cortical image representation. A neural threshold is applied to the contrast responses to include the effect of the neural contrast sensitivity. The resulting image representation is the base of a Bayesian pattern-recognition method robust to the presence of optical aberrations. The model is applied to images containing sets of letter optotypes at different scales, and the number of correct answers is obtained at each scale; the final output is the decimal Snellen VA. The model has no free parameters to adjust. The main input data are the eyes optical aberrations, and standard values are used for all other parameters, including the Stiles-Crawford effect, visual channels, and neural contrast threshold, when no subject specific values are available. When aberrations are large, Snellen VA involving pattern recognition differs from grating acuity, which is based on a simpler detection (or orientation-discrimination) task and hence is basically unaffected by phase distortions introduced by the optical transfer function. A preliminary test of the model in one subject produced close agreement between actual measurements and predicted VA values. Two examples are also included: (1) application of the method to the prediction of the VAin refractive-surgery patients and (2) simulation of the VA attainable by correcting ocular aberrations.

Modeling the Apparent Frequency-specific Suppression in Simple Cell Responses

Simple cells in cat striate cortex are selective for spatial frequency. It is widely believed that this selectivity arises simply because of the way in which the neurons sum inputs from the lateral geniculate nucleus. Alternate models, however, advocate the need for frequency-specific inhibitory mechanisms to refine the spatial frequency selectivity. Indeed, simple cell responses are often suppressed by superimposing stimuli with spatial frequencies that flank the neurons preferred spatial frequency. In this article, we compare two models of simple cell responses head-to-head. One of these models, the flanking-suppression model, includes an inhibitory mechanism that is specific to frequencies that flank the neurons preferred spatial frequency. The other model, the nonspecific-suppression model, includes a suppressive mechanism that is very broadly tuned for spatial frequency. Both models also include a rectification nonlinearity and both may include an additional accelerating (e.g., squaring) output nonlinearity. We demonstrate that both models can be consistent with the apparent flanking suppression. However, based on other experimental results, we argue that the nonspecific-suppression model is more plausible. We conclude that the suppression is probably broadly tuned for spatial frequency and that the apparent flanking suppression is actually due to distortions introduced by an accelerating output nonlinearity.

Probabilistic estimation of optical flow in multiple band-pass directional channels

Abstract Band-pass directional filters are not normally used as pre-filters for optical flow estimation because their orientation selectivity tends to increase the aperture problem. Despite this fact, here we obtain multiple estimates of the velocity by applying the classic gradient constraint to the output of each filter of a bank of six directional second-order Gaussian derivatives at three spatial resolutions. We obtain estimates of the velocity and of its associate covariance matrix, which define a full probability density function for the Gaussian case. We use this probabilistic representation to combine the resulting multiple velocity estimates, by first segmenting them in coherent motion processes, and then combining the estimates inside each coherent group assuming independence. Segmentation maintains the ability to represent multiple motions and helps to reject outliers so that the final estimates are robust, while combination helps to reduce the initial aperture problem. Results for synthetic and real sequences are highly satisfactory. Mean angular errors in complex standard sequences are similar to those provided by most published methods.

Probabilistic tracking of motion boundaries with spatiotemporal predictions

We describe a probabilistic framework for detecting and tracking motion boundaries. It builds on previous work (M.J. Black and D.J. Fleet, 2000) that used a particle filter to compute a posterior distribution over multiple, local motion models, one of which was specific for motion boundaries. We extend that framework in two ways: 1) with an enhanced likelihood that combines motion and edge support, 2) with a spatiotemporal model that propagates beliefs between adjoining image neighborhoods to encourage boundary continuity and provide better temporal predictions for motion boundaries. Approximate inference is achieved with a combination of tools: sampled representations allow us to represent multimodal non-Gaussian distributions and to apply nonlinear dynamics, while mixture models are used to simplify the computation of joint prediction distributions.

Error-in-variables likelihood functions for motion estimation

Over-determined linear systems with noise in all measurements are common in computer vision, and particularly in motion estimation. Maximum likelihood estimators have been proposed to solve such problems, but except for simple cases, the corresponding likelihood functions are extremely complex, and accurate confidence measures do not exist. This paper derives the form of simple likelihood functions for such linear systems in the general case of heteroscedastic noise. We also derive a new algorithm for computing maximum likelihood solutions based on a modified Newton method. The new algorithm is more accurate, and exhibits more reliable convergence behavior than existing methods. We present an application to affine motion estimation, a simple heteroscedastic estimation problem.

Bayesian pattern recognition in optically degraded noisy images

We present a novel Bayesian method for pattern recognition in images affected by unknown optical degradations and additive noise. The method is based on a multiscale/multiorientation subband decomposition of both the matched filter (original object) and the degraded images. Using this image representation within the Bayesian framework, it is possible to make a coarse estimation of the unknown optical transfer function, which strongly simplifies the Bayesian estimation of the original pattern that most probably generated the observed image. The method has been implemented and compared to other previous methods through a realistic simulation. The images are degraded by different levels of both random (atmospheric turbulence) and deterministic (defocus) optical aberrations, as well as additive white Gaussian noise. The Bayesian method proved to be highly robust to both optical blur and noise, providing rates of correct responses significantly better than previous methods.