16063444
Nonparametric Estimation and Simulation of Two-Dimensional Gaussian Image Textures
Abstract The work to be described is motivated by the need to simulate a variety of real–world image textures, all of which can be well approximated by stationary Gaussian random fields (SGRFs). Specifically, given an observed SGRF T , we wish to simulate SGRFs which look like and possess similar statistical properties to T . The main contribution of this paper is the development of an automatic and nonparametric spectrum estimation procedure which is able to produce an estimated spectrum of T in such a way that SGRFs simulated from this estimated spectrum have these desirable characteristics. Two special features of the procedure are: (i) it relies on a different risk function to that commonly used in nonparametric spectrum estimation, and (ii) it chooses its smoothing parameters by the technique of unbiased risk estimation. Results from a simulation study and a practical example demonstrate the good performance of the procedure. The practical example also illustrates how the proposed procedure can be combined with Monte Carlo testing to tackle target testing problems. Finally, the procedure is applied to the synthesis of some Brodatz textures, with some success.
18661216
A stabilized bandwidth selection method for kernel smoothing of the periodogram
One popular method for nonparametric spectral density estimation is to perform kernel smoothing on the periodogram, and one important component of this method is the choice of the bandwidth (or span) for smoothing. This paper proposes a new bandwidth selection method that is based on a coupling of the so-called plug-in and the unbiased risk estimation ideas. This new method is easy to describe, simple to implement, and does not impose severe conditions on the unknown spectrum. Numerical results suggest that this new method often outperforms some other commonly used bandwidth selection methods. The new methodology is also applied to choose the bandwidth for log-periodogram smoothing.
20836735
Kernel smoothing of periodograms under Kullback-Leibler discrepancy
Kernel smoothing on the periodogram is a popular nonparametric method for spectral density estimation. Most important in the implementation of this method is the choice of the bandwidth, or span, for smoothing. One idealized way of choosing the bandwidth is to choose it as the one that minimizes the Kullback-Leibler (KL) discrepancy between the smoothed estimate and the true spectrum. However, this method fails in practice, as the KL discrepancy is an unknown quantity. This paper introduces an estimator for this discrepancy, so that the bandwidth that minimizes the unknown discrepancy can be empirically approximated via the minimization of it. It is shown that this discrepancy estimator is consistent. Numerical results also suggest that this empirical choice of bandwidth often outperforms some other commonly used bandwidth choices. The same idea is also applied to choose the bandwidth for log-periodogram smoothing.
39601893
Smoothing parameter selection for smoothing splines: a simulation study
Smoothing splines are a popular method for performing nonparametric regression. Most important in the implementation of this method is the choice of the smoothing parameter. This article provides a simulation study of several smoothing parameter selection methods, including two so-called risk estimation methods. To the best of the author's knowledge, the empirical performances of these two risk estimation methods have never been reported in the literature. Empirical conclusions from and recommendations based on the simulation results will be provided. One noteworthy empirical observation is that the popular method, generalized cross-validation, was outperformed by another method, an improved Akaike Information criterion, that shares the same assumptions and computational complexity.
41225454
Segmenting images corrupted by correlated noise
Image segmentation is fundamental to many image analysis problems. It aims to partition a digital image into a set of non-overlapping homogeneous regions. This paper describes a new segmentation procedure which is designed to segment images corrupted by correlated noise. This procedure is based on Rissanen's (1989) minimum description length principle.
12361441
Computer-aided prototype system for nose surgery
Rhinoplasty, or surgery to reshape the nose, is one of the most common of all plastic-surgery procedures. Rhinoplasty can enhance a patient's appearance and self-confidence, may also correct a birth defect or injury, or help relieve some breathing problem. In this paper, we present a three-dimensional (3-D) surgical simulation system, which can assist surgeons in planning rhinoplasty procedures. This system employs computer graphics and image-processing techniques for the simulation of a rhinoplasty. Although the presented algorithms themselves are not new, the proposed system exploits the new idea to apply 3-D morphing for rhinoplasty, and simulation results are useful for the physicians. According to patients' expectation of what they would like their noses to look like, our system simulates expected results. Our tools provide quantitative measurements of a nose structure. Using these quantitative results, surgeons can arrange appropriate preoperative plans for patients. Finally, experimental results and experiences are reported to evaluate the usefulness of the proposed system.
767826
The Spectral Independent Components of Natural Scenes
We apply independent component analysis (ICA) for learning an efficient color image representation of natural scenes. In the spectra of single pixels, the algorithm was able to find basis functions that had a broadband spectrum similar to natural daylight, as well as basis functions that coincided with the human cone sensitivity response functions. When applied to small image patches, the algorithm found homogeneous basis functions, achromatic basis functions, and basis functions with overall chromatic variation along lines in color space. Our findings suggest that ICAm ay be used to reveal the structure of color information in natural images.
17578293
Representational strategy in the visual cortex
We generalized Daubechies' (see IEEE Transactions on Information Theory, vol.36, no.5, p.961-1004, 1990) results on 1D wavelets to 2D, and elucidated the conditions in which a family of Gabor wavelets will provide a complete representation of an image. We found that the phase space (scale, orientation, x, y) sampling density of the striate cortical simple cells is sufficiently dense to form a tight wavelet frame. This tight frame approximates the continuous wavelet transform, and its redundancy allows high resolution information to be represented in the low-resolution firings of the simple cells. We presented some experimental results to demonstrate this idea.<<ETX>>
10997807
Resource bounded symmetry of information revisited
The information contained in a string x about a string y is the difference between the Kolmogorov complexity of y and the conditional Kolmogorov complexity of y given x, i.e., I(x : y)=C(y)-C(y|x). The Kolmogorov-Levin Theorem says that I(x : y) is symmetric up to a small additive term. We investigate if this property also holds for several versions of polynomial time-bounded Kolmogorov complexity.We study symmetry of information for some variants of distinguishing complexity CD where CD(x) is the length of a shortest program which accepts x and only x. We show relativized worlds where symmetry of information does not hold in a strong way for deterministic and nondeterministic polynomial time distinguishing complexities CDpoly and CNDpoly. On the other hand, for nondeterministic polynomial time distinguishing complexity with randomness, CAMDpoly, we show that symmetry of information holds for most pairs of strings in any set in NP. Our techniques extend work of Buhrman et al. (Language compression and pseudorandom generators, in: Proc. 19th IEEE Conf. on Computational Complexity, IEEE, New York, 2004, pp. 15-28) on language compression by AM algorithms, and have the following application to the compression of samplable sources, introduced in Trevisan et al. (Compression of sample sources, in: Proc. 19th IEEE Conf. on Computational Complexity, IEEE, New York, 2004, pp. 1-15): any element x in the support of a polynomial time samplable source X can be given a description of size - log Pr[X = x] + O(log3 n), from which x can be recovered by an AM algorithm.
51888770
Statistical performance guarantees in large-scale cross-path packet switch
Recently, a quasi-static routing scheme called path switching was proposed for large-scale packet switch systems. The path-switched Clos network is called a cross-path switch. The cross-path switch is capable of supporting multirate and multicast traffic. In this paper, we develop a general framework for it to handle multimedia traffic. We study the statistical behavior of the cross-path switch using exponential bounded burstiness (EBB) processes as source session traffic models. With characterizing the service guarantees by service curves, we derive a set of statistical bounds on the delay, backlog and departure processes at the switch on a per-session basis. These bounds are necessary for providing per-session statistical quality of service (QoS) guarantees in the cross-path switch and achieving high system utilization.