2595966
Color demosaicking via directional linear minimum mean square-error estimation
Digital cameras sample scenes using a color filter array of mosaic pattern (e.g., the Bayer pattern). The demosaicking of the color samples is critical to the image quality. This paper presents a new color demosaicking technique of optimal directional filtering of the green-red and green-blue difference signals. Under the assumption that the primary difference signals (PDS) between the green and red/blue channels are low pass, the missing green samples are adaptively estimated in both horizontal and vertical directions by the linear minimum mean square-error estimation (LMMSE) technique. These directional estimates are then optimally fused to further improve the green estimates. Finally, guided by the demosaicked full-resolution green channel, the other two color channels are reconstructed from the LMMSE filtered and fused PDS. The experimental results show that the presented color demosaicking technique outperforms the existing methods both in PSNR measure and visual perception.
19420160
Multiscale LMMSE-based image denoising with optimal wavelet selection
In this paper, a wavelet-based multiscale linear minimum mean square-error estimation (LMMSE) scheme for image denoising is proposed, and the determination of the optimal wavelet basis with respect to the proposed scheme is also discussed. The overcomplete wavelet expansion (OWE), which is more effective than the orthogonal wavelet transform (OWT) in noise reduction, is used. To explore the strong interscale dependencies of OWE, we combine the pixels at the same spatial location across scales as a vector and apply LMMSE to the vector. Compared with the LMMSE within each scale, the interscale model exploits the dependency information distributed at adjacent scales. The performance of the proposed scheme is dependent on the selection of the wavelet bases. Two criteria, the signal information extraction criterion and the distribution error criterion, are proposed to measure the denoising performance. The optimal wavelet that achieves the best tradeoff between the two criteria can be determined from a library of wavelet bases. To estimate the wavelet coefficient statistics precisely and adaptively, we classify the wavelet coefficients into different clusters by context modeling, which exploits the wavelet intrascale dependency and yields a local discrimination of images. Experiments show that the proposed scheme outperforms some existing denoising methods.
29396765
Detection of LSB Steganography via Sample Pair Analysis
This paper introduces a new, principled approach to detecting LSB steganography in digital signals such as images and audio. It is shown that the length of hidden message embedded in the least significant bits of signal samples can be estimated with relatively high precision. The new steganalytic approach is based on some statistical measures of sample pairs that are highly sensitive to LSB embedding operations. The resulting detection algorithm is simple and fast. To evaluate the robustness of the proposed steganalytic approach, bounds on estimation errors are developed. Furthermore, the vulnerability of the new approach to possible attacks is also assessed, and counter measures are suggested.
17164296
Optimal context quantization in lossless compression of image data sequences
In image compression context-based entropy coding is commonly used. A critical issue to the performance of context-based image coding is how to resolve the conflict of a desire for large templates to model high-order statistic dependency of the pixels and the problem of context dilution due to insufficient sample statistics of a given input image. We consider the problem of finding the optimal quantizer Q that quantizes the K-dimensional causal context C/sub t/=(X/sub t-t1/,X/sub t-t2/,...,X/sub t-tK/) of a source symbol X/sub t/ into one of a set of conditioning states. The optimality of context quantization is defined to be the minimum static or minimum adaptive code length of given a data set. For a binary source alphabet an optimal context quantizer can be computed exactly by a fast dynamic programming algorithm. Faster approximation solutions are also proposed. In case of m-ary source alphabet a random variable can be decomposed into a sequence of binary decisions, each of which is coded using optimal context quantization designed for the corresponding binary random variable. This optimized coding scheme is applied to digital maps and /spl alpha/-plane sequences. The proposed optimal context quantization technique can also be used to establish a lower bound on the achievable code length, and hence is a useful tool to evaluate the performance of existing heuristic context quantizers.
36354030
Globally optimal uneven error-protected packetization of scalable code streams
In this paper, we present a family of new algorithms for rate-fidelity optimal packetization of scalable source bit streams with uneven error protection. In the most general setting where no assumption is made on the probability function of packet loss or on the rate-fidelity function of the scalable code stream, one of our algorithms can find the globally optimal solution to the problem in O(N/sup 2/L/sup 2/) time, compared to a previously obtained O(N/sup 3/L/sup 2/) complexity, where N is the number of packets and L is the packet payload size. If the rate-fidelity function of the input is convex, the time complexity can be reduced to O(NL/sup 2/) for a class of erasure channels, including channels for which the probability function of losing n packets is monotonically decreasing in n and independent erasure channels with packet erasure rate no larger than N/2(N + 1). Furthermore, our O(NL/sup 2/) algorithm for the convex case can be modified to rind an approximation solution for the general case. All of our algorithms do away with the expediency of fractional bit allocation, a limitation of some existing algorithms.
11758071
Algorithms for optimal multi-resolution quantization
Multi-resolution quantization is a way of constructing a progressively refinable description of a discrete random variable. The underlying discrete optimization problem is to minimize an expected distortion over all refinement levels weighted by the probability or importance of the descriptions of different resolutions. This research is motivated by the application of multimedia communications via variable-rate channels. We propose an O(rN2) time and O(N2 log N) space algorithm to design a minimum-distortion quantizer of r levels for a random variable drawn from an alphabet of size N. It is shown that for a very large class of distortion measures the objective function of optimal multi-resolution quantization satisfies the convex Monge property. The efficiency of the proposed algorithm hinges on the convex Monge property. But our algorithm is simpler (even though of the same asymptotic complexity) than the well-known SMAWK fast matrix search technique, which is the best existing solution to the quantization problem. For exponential random variables our approach leads to a solution of even lower complexity: O(rN) time and O(N log N) space, which outperforms all the known algorithms for optimal quantization in both multi- and single-resolution cases. We also generalize the multi-resolution quantization problem to a graph problem, for which our algorithm offers an efficient solution.
42284012
Efficient Algorithms for k-Terminal Cuts on Planar Graphs
AbstractThe minimum k-terminal cut problem is of considerable theoretical interest and arises in several
applied areas such as parallel and distributed computing, VLSI circuit design, and networking. In this paper
we present two new approximation and exact algorithms for this problem on an n-vertex undirected weighted
planar graph G. For the case when the k terminals are covered by the boundaries of m > 1 faces of G, we
give a min{O(n2 log n logm), O(m2n1.5 log2n + kn)} time algorithm with a (2–2/k)-approximation ratio
(clearly, m \le k). For the case when all k terminals are covered by the boundary of one face of G, we give an
O(nk3 + (n log n)k2) time exact algorithm, or a linear time exact algorithm if k = 3, for computing an optimal
k-terminal cut. Our algorithms are based on interesting observations and improve the previous algorithms when
they are applied to planar graphs. To our best knowledge, no previous approximation algorithms specifically
for solving the k-terminal cut problem on planar graphs were known before. The (2–2/k)-approximation
algorithm of Dahlhaus et al. (for general graphs) takes O(kn2 log n) time when applied to planar graphs. Our
approximation algorithm for planar graphs runs faster than that of Dahlhaus et al. by at least an O(k/logm)
factor (m \le k).
9160894
Geometric algorithms for static leaf sequencing problems in radiation therapy
The static leaf sequencing (SLS) problem arises in radiation therapy for cancer treatments, aiming to accomplish the delivery of a radiation prescription to a target tumor in the minimum amount of delivery time. Geometrically, the SLS problem can be formulated as a 3-D partition problem for which the 2-D problem of partitioning a polygonal domain (possibly with holes) into a minimum set of monotone polygons is a special case. In this paper, we present new geometric algorithms for a basic case of the 3-D SLS problem (which is also of clinical value) and for the general 3-D SLS problem. Our basic 3-D SLS algorithm, based on new geometric observations, produces guaranteed optimal quality solutions using Steiner points in polynomial time; the previously best known basic 3-D SLS algorithm gives optimal outputs only for the case without any Steiner points, and its time bound involves a multiplicative factor of a factorial function of the input. Our general 3-D SLS algorithm is based on our basic 3-D SLS algorithm and a polynomial time algorithm for partitioning a polygonal domain (possibly with holes) into a minimum set of x-monotone polygons, and has a fast running time. Experiments and comparisons using real medical data and on a real radiotherapy machine have shown that our 3-D SLS algorithms and software produce treatment plans that use significantly shorter delivery time and give better treatment quality than the current most popular commercial treatment planning system and the most well-known SLS algorithm. Some of our techniques and geometric procedures (e.g., for the problem of partitioning a polygonal domain into a minimum set of x-monotone polygons) are interesting in their own right.
31548532
Efficient Algorithms and Implementations for Optimizing the Sum of Linear Fractional Functions, with Applications
This paper presents an improved algorithm for solving the sum of linear fractional functions (SOLF) problem in 1-D and 2-D. A key subproblem to our solution is the off-line ratio query (OLRQ) problem, which asks to find the optimal values of a sequence of m linear fractional functions (called ratios), each ratio subject to a feasible domain defined by O(n) linear constraints. Based on some geometric properties and the parametric linear programming technique, we develop an algorithm that solves the OLRQ problem in O((m+n)log (m+n)) time. The OLRQ algorithm can be used to speed up every iteration of a known iterative SOLF algorithm, from O(m(m+n)) time to O((m+n)log (m+n)), in 1-D and 2-D. Implementation results of our improved 1-D and 2-D SOLF algorithm have shown that in most cases it outperforms the commonly-used approaches for the SOLF problem. We also apply our techniques to some problems in computational geometry and other areas, improving the previous results.
40889509
New Double-Byte Error-Correcting Codes for Memory Systems
Double-byte error-correcting codes over GF(q) were constructed by Dumer (1981, 1988, 1992, 1995), which have the parameters n=q/sup m-1/, r/spl les/2m+[m-1/3], m=2, 3, ..., when q is even, and have the parameters n=q/sup m/, r/spl les/2m+[m/3]+1, m=2; 3, ..., when q is odd, respectively. We construct a class of double-byte error-correcting codes over GF(2/sup i/), which have the following parameters: n=q/sup m/, r/spl les/2m+[m/3]+1, m=3, 4, .... So our constructions reduce the code redundancy of Dumer by one symbol, and we eliminate the disparity in code redundancies obtained for even and odd q. A decoding procedure for our codes is also considered.
15599036
Simultaneous Segmentation of Multiple Closed Surfaces Using Optimal Graph Searching
This paper presents a general graph-theoretic technique for simultaneously segmenting multiple closed surfaces in volumetric images, which employs a novel graph-construction scheme based on triangulated surface meshes obtained from a topological presegmentation. The method utilizes an efficient graph-cut algorithm that guarantees global optimality of the solution under given cost functions and geometric constraints. The method's applicability to difficult biomedical image analysis problems was demonstrated in a case study of co-segmenting the bone and cartilage surfaces in 3-D magnetic resonance (MR) images of human ankles. The results of our automated segmentation were validated against manual tracings in 55 randomly selected image slices. Highly accurate segmentation results were obtained, with signed surface positioning errors for the bone and cartilage surfaces being 0.02 +/- 0.11mm and 0.17 +/- 0.12mm, respectively.