Successive Elimination Algorithm Research Articles

Quantile Multi-Armed Bandits: Optimal Best-Arm Identification and a Differentially Private Scheme

We study the best-arm identification problem in multi-armed bandits with stochastic rewards when the goal is to identify the arm with the highest quantile at a fixed, prescribed level. First, we propose a successive elimination algorithm for strictly optimal best-arm identification, show that it is δ-PAC and characterize its sample complexity. Further, we provide a lower bound on the expected number of pulls, showing that the proposed algorithm is essentially optimal up to logarithmic factors. Both upper and lower complexity bounds depend on a special definition of the associated suboptimality gap, designed in particular for the quantile bandit problem - as we show, when the gap approaches zero, best-arm identification is impossible. Second, motivated by applications where the rewards are private information, we provide a differentially private successive elimination algorithm whose sample complexity is finite even for distributions with infinite support and characterize its sample complexity. Our algorithms do not require prior knowledge of either the suboptimality gap or other statistical information related to the bandit problem at hand.

Polymorphic types and effects with Boolean unification

We present a simple, practical, and expressive type and effect system based on Boolean constraints. The effect system extends the Hindley-Milner type system, supports parametric polymorphism, and preserves principal types modulo Boolean equivalence. We show how to support type inference by extending Algorithm W with Boolean unification based on the successive variable elimination algorithm. We implement the type and effect system in the Flix programming language. We perform an in-depth evaluation on the impact of Boolean unification on type inference time and end-to-end compilation time. While the computational complexity of Boolean unification is NP-hard, the experimental results demonstrate that it works well in practice. We find that the impact on type inference time is on average a 1.4x slowdown and the overall impact on end-to-end compilation time is a 1.1x slowdown.

Multi-level rate-constrained successive elimination algorithm tailored to suboptimal motion estimation in HEVC

In the context of motion estimation for video coding, successive elimination algorithms (SEAs) significantly reduce the number of candidates evaluated during motion estimation without altering the resulting optimal motion vector. Nevertheless, SEA is often only used in conjunction with exhaustive search algorithms (e.g., full search). In this paper, we combine the multi-level successive elimination algorithm (ML-SEA) and the rate-constrained successive elimination algorithm (RCSEA) and show that they can be advantageously applied to suboptimal search algorithms. We demonstrate that the savings brought about by the new multi-level RCSEA (ML-RCSEA) outweigh the pre-computational costs of this approach for the Test Zonal (TZ) Search algorithm found in the HM reference encoder. We propose a novel multi-level composition pattern for performing RCSEA on an asymmetric partitioning. We introduce a double-check mechanism for RCSEA, and show that on average, it avoids computing 71% of motion vector (MV) costs. We also apply the proposed ML-RCSEA to bi-predictive refinement search and leverage a cost-based search ordering to remove 56% of error metric computations, on average. When compared to the HM reference encoder, our experiments show that the proposed solution reduces the TZ Search time by approximately 45%, contributing to an average encoding time reduction of about 7%, without increasing the Bjøntegaard delta rate (BD-Rate).

Cost-Based Search Ordering for Rate-Constrained Motion Estimation Applied to HEVC

In the context of motion estimation for video coding, combining a successive elimination algorithm (SEA) with a motion estimation algorithm reduces the number of computed cost functions without impact on rate or distortion. The SEAs use the sum of absolute differences to eliminate motion vector candidates in the search area that cannot improve the current minimum. The novelty in this paper is that instead of relying on a static geometric pattern (i.e., like a spiral), we proposed a dynamic algorithm that creates a cost-based search orderings. A dynamic cost-based search ordering not only improves elimination but also allows for early termination which removes, on average, 61% of the block-matching loop iterations performed by the rate-constrained successive elimination algorithm (RCSEA). Our experiments show that the proposed solution is 5 times faster than the high efficiency video coding (HEVC) HM encoder software in full search mode with a 0.02% impact on BD-Rate. This is twice the speed of the HEVC HM software encoder using only the RCSEA.

Efficient motion estimation using two-bit transform and modified multilevel successive elimination

Reduced bit representations of video sequences are employed in order to mitigate the computational complexity of block matching algorithms. The idea is to explore computationally cheaper matching criteria than the conventional sum of absolute difference or fuzzy theory. Such low cost matching criteria result in substantial time saving and can therefore achieve real time video compression. To reduce the computational burden of such algorithms even further, we used them in orthogonal to the algorithms which reduces the number of search points in the search window. The speedup in computation as a result of using two-bit transform is rectified by imposing a modified version of multilevel successive elimination algorithm in orthogonal form. Experimental results show that the numbers of search points can be reduced by an average of 95% for sequences with low motion content and by an average of 85% for sequences with relatively high motion content. For all the results the same peak-signal-to-noise ratio of the reconstructed frames is maintained as that of the two-bit transform.

Fast motion estimation algorithm using multilevel distortion search in Walsh–Hadamard domain

Block-matching motion estimation (BME) can efficiently reduce the temporal redundancy between the successive video sequences in video compression coding system. In this study, a fast BME algorithm using multilevel distortion search in Walsh–Hadamard domain is proposed to reduce the computational burden and speed up coding process. First, the proposed algorithm divides the block into several sub-blocks. Then, the Walsh–Hadamard transform is applied to these sub-blocks. Finally, the proposed algorithm calculates the partial block matching distortion by utilising a novel back diagonal search scheme which can quickly reject unnecessary candidate block in a multilevel manner. Experimental results show that the proposed algorithm effectively reduces the number of operations in block distortion calculation meanwhile maintains the best motion estimation matching quality. Compared with the full search, the proposed algorithm can reduce 87.19% computational complexity without any degradation of the peak signal to noise ratio. In addition, compared with the partial distortion search algorithm, successive elimination algorithm, multilevel successive elimination algorithm and the transform-domain successive elimination algorithm, the proposed algorithm can also save 68.27, 70.09, 37.81 and 37.44% computational complexity, respectively. Moreover, the proposed algorithm can also be easily incorporated into any block-based template search motion estimation algorithm.

All-layer search algorithm using mean inequality and improved checkerboard partial distortion search for fast motion estimation

Block-matching motion estimation algorithm is used in many video compression coding systems because it could greatly reduce the temporal redundancy between the consequent video sequences. In this paper, an all-layer search algorithm using mean inequality and improved checkerboard partial distortion search scheme for fast block-matching motion estimation is proposed. A layer in the proposed method refers to a processed image which is derived from the reference frame or the adjacent lower layer. Firstly, the proposed algorithm constructs all layers from the reference frame or the adjacent lower layer by summing up all pixels over a sub-block. Then, a new mean inequality elimination method is introduced to reject a lot of unnecessary candidate search points on the top layers before calculating the real block matching distortion. Finally, the proposed algorithm utilizes an improved checkerboard partial distortion search scheme in the process of the real block distortion calculation on the following layers to further reduce the amount of computation. Experimental results show that the proposed algorithm can effectively reduce the computational complexity of motion estimation meanwhile guarantee the matching quality compared to other motion estimation algorithms. Compared to the full search algorithm, the proposed algorithm can reduce 97.30 % computational complexity with a negligible degradation of the peak signal to noise ratio (PSNR). Compared to the diamond search algorithm, directional gradient descent search algorithm, partial distortion search algorithm, transform-domain successive elimination algorithm and two-layer motion estimation algorithm, the proposed algorithm can also save 63.56 %, 52.73 %, 92.87 %, 85.77 % and 33.96 % computational complexity, respectively.

Successive Elimination Algorithm for Constrained One-bit Transform Based Motion Estimation Using the Bonferroni Inequality

Successive Elimination Algorithm for Constrained One-bit Transform Based Motion Estimation Using the Bonferroni Inequality

Multilevel motion estimation based on distortion measure in transform domain

A transform-domain successive elimination algorithm for block-based motion estimation (ME) is proposed. First, a method is introduced for calculating the sum of squared differences in the transform domain. Then, based on this method, a new transform-domain criterion is proposed to eliminate impossible candidates as early as possible. Experimental results show that the proposed algorithm speeds up the ME process by up to a factor of 10 compared with the conventional full search algorithm.

Simple low-dimensional features approximating NCC-based image matching

This paper proposes new low-dimensional image features that enable images to be very efficiently matched. Image matching is one of the key technologies for many vision-based applications, including template matching, block motion estimation, video compression, stereo vision, image/video near-duplicate detection, similarity join for image/video database, and so on. Normalized cross correlation (NCC) is one of widely used method for image matching with preferable characteristics such as robustness to intensity offsets and contrast changes, but it is computationally expensive. The proposed features, derived by the method of Lagrange multipliers, can provide upper-bounds of NCC as a simple dot product between two low-dimensional feature vectors. By using the proposed features, NCC-based image matching can be effectively accelerated. The matching performance with the proposed features is demonstrated using an image database obtained from actual broadcast videos. The new features are shown to outperform other methods: multilevel successive elimination algorithm (MSEA), discrete cosine transform (DCT) coefficients, and histograms, achieving very high precision while only slightly sacrificing recall.

Analysis of Image Inpainting Techniques with Exemplar, Poisson, Successive Elimination and 8 Pixel Neighborhood Methods

This paper discusses removing large objects from digital images and fills the hole that is left behind in a visually plausible way. We present a novel and efficient algorithm that fills the hole by exemplar-based synthesis. Here the simultaneous propagation of texture and structure information is achieved by a single, efficient algorithm. The texture image is repaired by the exemplar –based method; for the structure image, the Laplacian operator is employed to enhance the structure information, and the Laplacian image is inpainted by the exemplar-based algorithm, followed by a reconstruction based on the Poisson equation. To improve the computational efficiency of our algorithm we go for successive elimination algorithm (SEA). In 8 pixel neighborhood method, identifying central pixel value by investigating surrounded 8 neighborhood pixel properties like color variation, repetition, intensity and direction. Finally we compare speed and accuracy of a picture enhancement using 8 pixel neighborhood with exemplar based poisson & successive elimination method

2:1 Candidate Position Subsampling Technique for Fast Optimal Motion Estimation

The candidate position subsampling technique (CPST) basically chooses candidates in a search window at a sampling rate. The 2:1 CPST chooses half the candidates, and then selects one or more candidates that are considered as to be close to the optimal motion vector before conducting a fine search. The fine search is conducted by checking four neighbors of the chosen candidate(s) referred to as winner(s). The CPST can be combined with a fast optimal block-matching algorithm, such as the multilevel successive elimination algorithm (MSEA), in order to reduce the number of computations used in rejecting the nonbest candidate. We propose a new 2:1 CPST fitted to the MSEA. The proposed algorithm adopts a new condition for the winner which helps to find the best candidate efficiently. Moreover, a fast motion estimation step is used to reduce the number of computations of the MSEA, and the peak signal-to-noise ratio (PSNR) compensation step is adopted to guarantee that the PSNR performance of the proposed algorithm is very close to that of the full search. Experimental results show that the proposed algorithm reduces the computational loads of the MSEA by 47.26% on average with only -0.027 dB PSNR degradation in the worst case.

DG Impact on Investment Deferral: Network Planning and Security of Supply

Despite the technical challenges in properly accommodating distributed generation (DG), one of the major and well-recognized benefits is the ability of DG to defer future demand-related network investment. It is, however, often poorly represented in existing planning approaches and analysis ignores the potential security of supply benefits. Here, a novel, more integrated, approach is presented wherein reinforcements required by system security standards (e.g., N - 1) are also taken into account. The DG contributions to system security provided by U.K. Engineering Recommendation P2/6 are adopted, enabling the methodology to quantify the deferment produced by DG considering both demand growth- and system security-related investment. The methodology employs the successive elimination algorithm together with multistage planning and is applied to a generic, meshed, U.K. distribution network. Results show that, despite differences between technology types, significant economic benefits can be harnessed when strategically incorporating DG at the planning stage.

Successive elimination algorithm for two-bit transform-based motion estimation

A successive elimination algorithm for two-bit transform (2BT) based motion estimation (ME) is proposed. By mathematically deriving the lower bound for2BT-based matching criterion, we can discard the impossible candidates earlier and save computations substantially. Experimental results show that although the performance of the proposed algorithm is the same as that of the full search 2BT (FS-2BT) based ME algorithm, the computational complexity has been reduced significantly.

Content-Aware Fast Motion Estimation Algorithm

In this paper, we propose the Content-Aware Fast Motion Estimation Algorithm (CAFME) that can reduce computation complexity of motion estimation (ME) in H.264/AVC while maintaining almost the same coding efficiency. Motion estimation can be divided into two phases: searching phase and matching phase. In searching phase, we propose the Simple Dynamic Search Range Algorithm (SDSR) based on video characteristics to reduce the number of search points (SP). In matching phase, we integrate the Successive Elimination Algorithm (SEA) and the integral frame to develop a new SEA for H.264/AVC video compression standard, called Successive Elimination Algorithm with Integral Frame (SEAIF). Besides, we also propose the Early Termination Algorithm (ETA) to early terminate the motion estimation of current block. We implement the proposed algorithm in the reference software JM9.4 of H.264/AVC and the experimental results show that our proposed algorithm can reduce the number of search points about 93.1%, encoding time about 42%, while maintaining almost the same bitrate and PSNR.

Fast Optimal Motion Estimation Based on Gradient-Based Adaptive Multilevel Successive Elimination

In this paper, we propose a fast and optimal solution for block motion estimation based on an adaptive multilevel successive elimination algorithm. This algorithm is accomplished by applying a modified multilevel successive elimination algorithm (SEA) with the elimination order determined by the sum of the gradient magnitudes of each subblock and the elimination process terminated by comparing the above sum with a threshold. In addition a fast approximate motion estimation method and the accumulated distortion scheme are employed to make the proposed algorithm even more efficiently. Experimental results show that the proposed adaptive multilevel successive elimination strategy (AdaMSEA) algorithm significantly outperforms other previous optimal motion estimation algorithms, including SEA, MSEA, and FGSE on a wide variety of video sequences. Finally, we modify the proposed AdaMSEA to an approximate motion estimation algorithm to achieve very fast computational speed, and the experimental results show superior performance of this approximate algorithm over some fast motion estimation algorithms.

Adaptive Fast Full Search Algorithm using Partitioned Region and Optimized Search Order

In this paper, an adaptive fast full search algorithm is proposed. The fast full search algorithm only reduces the complexity of the block matching algorithm used for motion estimation of video coding. Since the spiral search method used in conventional algorithms starts searching at the center of the search range and then moves the candidate position to estimate motion pixel by pixel, it is best for slow motion pictures. The spiral search method usually has better performance than a full search using the raster scan search method. However, the proposed algorithm is best for sequences which have numerous rapid motions. In the first of two proposed stages, using a predicted motion vector, we determine the region search order based on gradient distances among all regions after partitioning the search range. In the second stage, by means of region order, the matching error of all candidate positions is calculated in an optimized search order which is derived from the local image complexity of the current macro-block to search. The proposed algorithm, based on a multilevel successive elimination algorithm, reduces the complexity of motion estimation up to 96.6% on average, compared with the conventional full search algorithm without any loss of image.

Noise variance adaptive successive elimination algorithm for block motion estimation: application for video surveillance

In a practical video encoder, a video sequence obtained from a camera inevitably conveys noise. The noise term degrades not only image quality but also coding efficiency. Based on the statistical analysis of noise signal, a two-stage noise variance adaptive successive elimination algorithm (SEA) for block motion estimation is presented. To reduce the additional computation cost required for video noise estimation, it is embedded into the process of block matching using Kalman filtering. Simulation results demonstrate that the performance of the proposed algorithm is close to that of the SEA, whereas the computational complexity has been significantly reduced.

Lossy Strict Multilevel Successive Elimination Algorithm for Fast Motion Estimation

This paper presents a simple and effective method to further reduce the search points in multilevel successive elimination algorithm (MSEA). Because the calculated sea values of those best matching search points are much smaller than the current minimum SAD, we can simply increase the calculated sea values to increase the elimination ratio without much affecting the coding quality. Compared with the original MSEA algorithm, the proposed strict MSEA algorithm (SMSEA) can provide average 6.52 times speedup. Compared with other lossy fast ME algorithms such as TSS and DS, the proposed SMSEA can maintain more stable image quality. In practice, the proposed technique can also be used in the fine granularity SEA (FGSEA) algorithm and the calculation process is almost the same.

Threshold-based successive elimination algorithm for block motion estimation

The successive elimination algorithm (SEA) has already proved successful in block motion estimation. This paper presents a simple and efficient algorithm called the threshold-based SEA as a search engine to take advantage of the simplicity of the SEA while avoiding its redundant computation. In addition, the threshold-based SEA utilizes a threshold adaptation mechanism to efficiently distribute the available computational power of the employed codec to blocks of video sequences. Since the threshold-based approach is performed at each search candidate block, it can be combined not only with the SEA but also with other fast algorithms, including the three-step search, the block-based gradient descent search, and the diamond search. Depending on the motion activity in the sequences, experimental results indicate that the threshold-based approach can uniformly achieve a quality improvement over the original SEA for the same computation.