Modeling Space-variant Visual Acuity And Image Compression As Eigenvalue Problems

Established theoretical reasons recommend functions that are limited in space and spatial frequency as models for receptive fields of visual neurons. On the basis of an interpretation of spread as variance and via analogy to quantum mechanics, the Gabor functions are often stated to be maximally limited in space and spatial frequency (Daugman, 1985). Some Gabor functions indeed resemble receptive fields in V1, but this view provides little insight into why V1 receptive fields have only a small number of lobes, nor into receptive field shape beyond V1. Here we consider an alternative interpretation of “limited in space and spatial frequency.” We consider a function to be “confined” in space (or spatial frequency) if it is unchanged by windowing in space (or spatial frequency). While no function can be simultaneously confined in both space and spatial frequency, there is a rigorous sense in which the 2-dimensional Hermite functions achieve simultaneous confinement as nearly as possible. The 2-dimensional Hermite functions are a complete basis set and form a natural hierarchy. The first levels of this hierarchy contain functions that resemble Gabor functions with a small number of lobes, and thus resemble V1 receptive fields. Further down the hierarchy are intrinsically 2-dimensional functions, some of which resemble the non-Cartesian gratings, to which some V4 neurons respond preferentially (Gallant, 1996). In addition to their many interesting mathematical properties, the two-dimensional Hermite functions allow for efficient (“sparse”) local synthesis of images, including natural scenes, faces, and letters. While we make no claim that this view suffices to account for receptive field structure, we suggest that it provides a framework for a principled study of receptive fields, and that it is useful to think of receptive fields (along the V1-to-V2-to-V4 pathway) as not only expanding, but also increasing in their combined space-bandwidth aperture.

In this study, we focus on the fractal property of recurrence networks constructed from the two-dimensional fractional Brownian motion (2D fBm), i.e., the inter-system recurrence network, the joint recurrence network, the cross-joint recurrence network, and the multidimensional recurrence network, which are the variants of classic recurrence networks extended for multiple time series. Generally, the fractal dimension of these recurrence networks can only be estimated numerically. The numerical analysis identifies the existence of fractality in these constructed recurrence networks. Furthermore, it is found that the numerically estimated fractal dimension of these networks can be connected to the theoretical fractal dimension of the 2D fBm graphs, because both fractal dimensions are piecewisely associated with the Hurst exponent H in a highly similar pattern, i.e., a linear decrease (if H varies from 0 to 0.5) followed by an inversely proportional-like decay (if H changes from 0.5 to 1). Although their fractal dimensions are not exactly identical, their difference can actually be deciphered by one single parameter with the value around 1. Therefore, it can be concluded that these recurrence networks constructed from the 2D fBms must inherit some fractal properties of its associated 2D fBms with respect to the fBm graphs.

SUMMARY Two-dimensional phase unwrapping (PU) process usually causes a noise-induced distortion in the geographical information of a wrapped phase image obtained by, for example, interferometric synthetic aperture radar (InSAR). This paper presents a novel method to reduce the phase-unwrapping distortion by being based on two-dimensional fractional Brownian motion (fBm) theory. The method incorporates fractal geometry estimation with conventional global-transform PU. For the spatialfrequency spectrum of an observed phase image, we estimate the fractal dimension by assuming an almost constant dimension over the image. Then, according to the estimation, we compensate the distorted spectrum of the tentatively computed global PU result. We obtain a better topographical map as the inverse Fourier transform of the compensated spectrum. It is demonstrated that the proposed method increases the signal-to-noise ratio of PU results for simulated data with various noise levels. Evaluations on an actual InSAR phase image also show that the method significantly improves the quality of the conventional global-transform PU result, in par

This paper presents a novel method to reduce the phase-unwrapping (PU) distortion by being based on two-dimensional fractional Brownian motion (fBm) theory. The method incorporates fractal geometry estimation to the result of conventional global-transform PU (GTPU). For the spatial-frequency spectrum of an observed phase image, we estimate the fractal dimension, by assuming an almost constant dimension over the image, and compensate the distorted spectrum of a GTPU result. It is demonstrated that the proposed method increases the signal-to-noise ratio of PU results for simulated data with various noise levels. Evaluations on an actual InSAR phase image also show that the method significantly improves the quality of the conventional GTPU result in its fine structure in particular.

In this paper, we study the least-squares estimation problem for the Vasicek model driven by the complex fractional Brownian motion where is a two-dimensional fractional Brownian motion with Hurst parameter We obtain the strong consistency and asymptotic normality of and using the Garsia–Rodemich–Rumsey inequality and complex fourth moment theorems.

Markov chainMonteCarlo (MCMC)methodshavebeenaround for almost as longasMonte Carlo techniques, even though their impact on statistics was not truly felt until the very early 1990s, except in the specialized fields of spatial statistics and image analysis, where those methods appeared earlier. The emergence of Markov based techniques in physics is a story that remains untold within this survey (see Landau and Binder, 2005). Also, we will not enter into a description of MCMC techniques, unless they have some historical link, as the remainder of this volume covers the technical aspects.Acomprehensive treatment with further references can also be found in Robert and Casella (2004). We will distinguish between the introduction of Metropolis-Hastings based algorithmsand those related to Gibbs sampling, since they each stem from radically different origins, even though their mathematical justification via Markov chain theory is the same. Tracing the development of Monte Carlo methods, we will also briefly mention what we might call the “second-generation MCMC revolution.” Starting in the mid to late 1990s, this includes the development of particle filters, reversible jump and perfect sampling, and concludes with more current work on population or sequential Monte Carlo and regeneration and the computing of “honest” standard errors. As mentioned above, the realization that Markov chains could be used in a wide varietyof situations only came (tomainstream statisticians)withGelfand and Smith (1990), despite earlier publications in the statistical literature such as Hastings (1970), Geman and Geman (1984), and Tanner and Wong (1987). Several reasons can be advanced: lack of computing machinery (think of the computers of 1970!), or background onMarkov chains, or hesitation to trust in the practicality of themethod. It thus required visionary researchers like Gelfand and Smith to convince the community, supported by papers that demonstrated, through a series of applications, that the method was easy to understand, easy to implement and practical (Gelfand et al., 1990, 1992; Smith and Gelfand, 1992; Wakefield et al., 1994). The rapid emergence of the dedicated BUGS (Bayesian inference using Gibbs sampling) software as early as 1991, when a paper on BUGS was presented at the Valencia meeting, was another compelling argument for adopting, at large, MCMC algorithms.∗Monte Carlo methods were born in Los Alamos, New Mexico, during World War II, eventually resulting in theMetropolis algorithm in the early 1950s. WhileMonte Carlo methods were in use by that time, MCMC was brought closer to statistical practicality by the work of Hastings in the 1970s. What can be reasonably seen as the first MCMC algorithm is what we now call theMetropolis algorithm, published by Metropolis et al. (1953). It emanates from the same group of scientists who produced the Monte Carlo method, namely the research scientists of Los Alamos, mostly physicists working on mathematical physics and the atomic bomb. MCMC algorithms therefore date back to the same time as the development of regular(MC only) Monte Carlo methods, which are usually traced to Ulam and von Neumann in the late 1940s. StanislawUlam associates the original ideawith an intractable combinatorial computation he attempted in 1946 (calculating the probability of winning at the solitaire card game). This ideawas enthusiastically adopted by John vonNeumann for implementationwith direct applications to neutron diffusion, the name “Monte Carlo” being suggested by Nicholas Metropolis. Eckhardt (1987) describes these early Monte Carlo developments, and Hitchcock (2003) gives a brief history of the Metropolis algorithm. These occurrences very closely coincide with the appearance of the very first general-purpose digital computer, the ENIAC,which came to life in February 1946, after three years of construction. The Monte Carlo method was set up by von Neumann, who was using it on thermonuclear and fission problems as early as 1947. That same year, Ulam and vonNeumann invented inversion andaccept-reject techniques (also recounted inEckhardt, 1987) to simulate from nonuniform distributions. Without computers, a rudimentary version invented by Fermi in the 1930s went unrecognized (Metropolis, 1987). Note also that, as early as 1949, a symposiumonMonteCarlowas supported byRand, theNational Bureau of Standards, and theOakRidge laboratory and thatMetropolis andUlam (1949) published the very first paper about the Monte Carlo method.

This paper presents an analytical method for image analysis and reconstruction of still images using the complex Gabor (1946) wavelets. The Gabor wavelet is one of the most widely used complex wavelets, and has been used for image texture analysis and segmentation, motion estimation, image analysis, signal processing and face authentication. However no straightforward method is available to extract the wavelet coefficients. An analytical method for image expansion-reconstruction of still images using the Gabor function is presented for the first time.

Spatial filters that mimic receptive fields of visual cortex neurons provide an efficient representation of achromatic image structure, but the extension of this idea to chromatic information is at an early stage. Relatively few studies have looked at the statistical relationships between the modeled responses to natural scenes of the luminance (LUM), red-green (RG), and blue-yellow (BY) postreceptoral channels of the primate visual system. Here we consider the correlations among these channel responses in terms of pixel, first-order, and second-order information. First-order linear filtering was implemented by convolving the cosine-windowed images with oriented Gabor functions, whose gains were scaled to give equal amplitude response across spatial frequency to random fractal images. Second-order filtering was implemented via a filter-rectify-filter cascade, with Gabor functions for both first- and second-stage filters. Both signed and unsigned filter responses were obtained across a range of filter parameters (spatial frequency, 2-64 cycles/image; orientation, 0-135 degrees). The filter responses to the LUM channel images were larger than those for either RG or BY channel images. Cross correlations between the first-order channel responses and between the first- and second-order channel responses were measured. Results showed that the unsigned correlations between first-order channel responses were higher than expected on the basis of previous studies and that first-order channel responses were highly correlated with LUM, but not with RG or BY, second-order responses. These findings imply that course-scale color information correlates well with course-scale changes of fine-scale texture.

This issue of Mathematical Geology is the outcome of the September 1999 BioGeoImages conference held in Dijon (France) at the University of Burgundy. The aim of this conference was to bring together people who did not have the opportunity to meet frequently, although they were working on different topics but using similar methods. Geologists, biologists (paleontologists), mathematicians, and computer scientists working on the shape and distribution of natural objects using image analysis, met during 3 days to exchange methods and points of view on rock forming features, from fossils to crystals. Form is defined as the visible appearance of an object, the whole of the contours resulting from the structure of its parts. Biologists and geologists recognize that the form of an object concentrates a lot of information about its structures and its past evolution. However, as pointed out by Alain Boutot (1993, p. 23), form is an idea that is fundamentally qualitative. Form is a rupture, a break between the object and the space in which it evolves or exists. This discontinuity is the source of morphogenesis, and a discontinuity is measurable or at least observable. It is the abrupt transition from one state to another. Therefore form can be projected, highlighted, or illuminated in various ways. If the entire form cannot be manipulated, certain of its characteristics or features can be extracted in a metric space. This is the aim of morphometry, the study of shape. Morphometry is not the measurement of the form itself but of its external and perceptible characteristics, i.e., in a first approximation, its shape or morphology. Morphology is defined as the study of the configuration and the external structure of the object, i.e., its appearance. The term comes from the Greek μoρφη (form) and λoγ oσ (study). Form in Greek (μoρφη) makes reference to the mythological entity Morpheus, one of the many children of the god of sleep Hypnos. Morpheus causes his sleeping subjects to dream and captures

Text detection in natural and complex images play an important role in analysis of image. Text information appears everywhere like product labels, documents, scene images etc. It will be very difficult for visually impaired person to find text region in an image. This problem should be addressed because it cannot assume that the captured image contains only text. This paper presents camera-based text reading framework which helps visually impaired people to read texts in natural scenes, product labels etc. Here, task is divided into two steps i.e. text detection and text recognition. Text detection involves text localization phase. Firstly, we binarize the image. Geometric and stroke width filtering removes non text regions an image. Segmented text region in a cluttered scene is binarized and recognized by optical character recognition. Recognized texts are output to the visually impaired people in speech. Experimental result shows that proposed method offers better performance in text recognition.

All the elements of a Fourier analysis can be derived from the experiments of Graham and Robson on contrast sensitivity. Once their experiment is posed as an eigenvalue problem, a complete orthonormal set of eigenfunctions results from solving the associated differential equation. Neither sine and cosine nor Gabor functions result. Instead, the Hermite functions arise as the eigenfunctions of a space-variant differential operator used to model the contrast sensitivity of human observers. These functions, up to a constant, are their own Fourier transforms, and in principle can be used to exactly represent the Fourier transform of naturally occurring visual images.

Visual perception is often conceptualized as the analysis of static images which are acquired during fixations. These images are then spatially decomposed into their basic components, which form the fundament of visual perception. Understanding these spatial mechanisms has been a central aim of pattern vision, and has led to a successful and widely adopted standard model of spatial vision. The spatial view on pattern vision, however, overlooks a key aspect of visual processing: the eyes are never still. Even during fixations, involuntary eye movements incessantly modulate the visual input. These eye movements challenge the assumption that visual processing can occur independently of motion. In recent years, empirical evidence has accumulated which suggests that fixational eye movements, particularly ocular drift, actively shape visual processing. Building on these findings, this thesis argues that ocular drift is essential to how the visual system encodes spatial structure, even in the absence of external motion. It calls for a shift from static to active, spatiotemporal models of pattern vision. To support this shift, it integrates computational modeling, psychophysics, and new experimental tools to explore how ocular drift influences edge and pattern perception. The first part of this thesis revisits foundational assumptions in spatial vision. In a first study, it presents a proof-of-concept model that extends a standard spatial vision model by ocular drift and temporal processing. The active model components facilitate edge extraction, but also reveal limitations in current datasets which cannot clearly distinguish between static and active accounts of pattern vision. In response, the next two studies introduce new software tools and a benchmark dataset that specifically target the spatial frequency selective mechanisms underlying pattern vision. Using this dataset, the fourth study explicitly contrasts spatial and active accounts of pattern vision. The results show that incorporating ocular drift improves predictions of human edge sensitivity and reveals that traditional models may rely on compensatory biases to account for the absence of these eye movements. The final study introduces a behavioral task in which participants trace edges in natural scenes. This approach enables the study of pattern vision in more naturalistic contexts while maintaining the analytical rigor of traditional psychophysics through signal detection theory. The resulting dataset supports both standard analyses and investigations into individual differences and the visual features that guide edge perception in real-world settings. Altogether, this thesis integrates insights from active perception into a mechanistically grounded framework of pattern vision. It redefines early visual processing as an active, embodied process shaped by the observer’s own movements. These findings challenge static models of early visual processes and advocate for a broader paradigm shift that places motion, context, and environmental interaction at the core of perception. Finally, it lays a foundation for future research into active models of vision, offering both theoretical direction and practical tools to study visual perception under more natural conditions.

In the present study, we investigated the detection of contours defined by constant curvature and the statistics of curved contours in natural scenes. In Experiment 1, we examined the degree to which human sensitivity to contours is affected by changing the curvature angle and disrupting contour curvature continuity by varying the orientation of end elements. We find that (1) changing the angle of contour curvature decreased detection performance, while (2) end elements oriented in the direction (i.e., clockwise) of curvature facilitated contour detection regardless of the curvature angle of the contour. In Experiment 2 we further established that the relative effect of end—element orientation on contour detection was not only dependent on their orientation (collinear or cocircular), but also their spatial separation from the contour, and whether the contour shape was curved or not (i.e., C-shaped or S-shaped). Increasing the spatial separation of end-elements reduced contour detection performance regardless of their orientation or the contour shape. However, at small separations, cocircular end-elements facilitated the detection of C-shaped contours, but not S-shaped contours. The opposite result was observed for collinear end-elements, which improved the detection of S- shaped, but not C-shaped contours. These dissociative results confirmed that the visual system specifically codes contour curvature, but the association of contour elements occurs locally. Finally, we undertook an analysis of natural images that mapped contours with a constant angular change and determined the frequency of occurrence of end elements with different orientations. Analogous to our behavioral data, this image analysis revealed that the mapped end elements of constantly curved contours are likely to be oriented clockwise to the angle of curvature. Our findings indicate that the visual system is selectively sensitive to contours defined by constant curvature and that this might reflect the properties of curved contours in natural images.

Prior knowledge about anticipated distortions and their corresponding human opinion scores is needed in the most general purpose no-reference image quality assessment algorithms. When creating the model, all distortion types may not be existed. Predicting the quality of distorted images in practical no-reference image quality assessment algorithms is devised without prior knowledge about images or their distortions. In this study, a blind/no-reference opinion and distortion unaware image quality assessment algorithm based on natural scenes is developed. The proposed approach uses a set of novel features to measure image quality in a spatial domain. The extracted features which are from the scenes gist are formed using Weibull distribution statistics. When testing the proposed algorithm on LIVE database, experiments show that it correlates well with subjective opinion scores. They also show that the proposed algorithm significantly outperforms the popular full-reference peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) methods. Not only do the results reasonably well compete with the recently developed natural image quality evaluator (NIQE) model, but also outperform it.

When creating image quality assessment metric (IQA) no confirmation all distortion types are available. Non-specific distortion blind/no-reference (NR) IQA algorithms mostly need prior knowledge about anticipated distortions. This paper introduce a generic and distortion unaware (DU) approach for IQA with No Reference (NR). The approach uses three different measuring features which are initiated from the gist of natural scenes (NS) using Log-derivatives of the parameters; a general Gaussian distribution model, two sharpness functions, and Weibull distribution. All features were analyzed and co mpared together to examine their performance. When calibrating the proposed features performance on LIVE database, experiments show they have good contribution to the state of the art IQA and they outperform the popular full-reference peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) methods. Also they show sharpness features are the best when assess both prediction monotonicity and predict accuracy evaluation among the three features categories. Besides they show asymmetric generalized Gaussian distribution (AGGD) based features have the best correlation with differential mean opinion score.