Sum Of The Absolute Differences Research Articles

A Method of Constructing Models for Estimating Proportions of Citrus Fruit Size Grade Using Polynomial Regression

Estimating the fruit size is an important factor because it directly influences size-specific yield estimation, which would be useful for pricing in the market. In this paper, it was considered a method of constructing models for estimating the proportion of fruit size grades of citrus using polynomial regression. In order to construct models, curvilinear regressions were performed, utilizing the fruit diameters of a kind of citrus (Citrus junos Sieb. ex Tanaka) in the harvest. The constructed models were validated by comparison with another model, which was constructed using a combination of four datasets obtained from three orchards differing in the number of fruit sets. The estimation model’s accuracy (EMA, defined as the sum of the absolute difference between the actual and estimated proportions of each grade) was used for the evaluation of constructed models. The EMAs of 14 models applied to 28 validation data were ranging from 2.0% to 6.1%. In all validations, the proportions of fruit size grade were insignificant at a 5% level by Pearson’s chi-square test. Additionally, a comparison of EMAs differing in the number of trees by the constructed models showed that most were within EMA ≤ 10.0% in the case calculated by 10 trees. Validation of five farmers’ orchards indicated that the EMA of two was within 10.0%, and the EMA of three was at 11.3 to 12.5%. These results revealed that the constructed models could be applied to orchards for differing numbers of fruit sets. The acceptable accuracy was derived by at least over 10 trees investigated at one time.

Estimating the Hydraulic Conductivity of jointed rock mass using Genetic Programming

Ground engineering through injection of cementitious grouts or polymer resins is an integral part of fractured rock mass stabilisation by improving its maximum load carrying capacity, stiffness, cohesiveness and reduction in permeability. To optimise product delivery and achieve a high penetrability of product into the rock mass, it is imperative to understand the permeability characteristics or hydraulic conductivity of the rock mass. The hydraulic conductivity of the rock mass also dictates the type of polyurethane (PU) or cement-based products to be injected. For this purpose, a Packer test has to be conducted to measure the hydraulic conductivity of a rock formation which is an expensive and time-consuming process. Alternatively, a number of empirical methods that use rock mass classifications and rock joint properties Rock Quality Designation (RQD), Q-system (Q), Geological Strength Index (GSI), Joint Spacing (JS), Joint Aperture (a) proposed by a number of researchers that are capable of predicting hydraulic conductivity (HC). In this research, a predictive model between rock mass properties and HC is proposed using new approach - genetic programming (GP). For this purpose, a database of rock mass parameters including RQD, Q, GSI, JS, Joint Aperture (a), Second Permeability Index (SPI) and Packer test results available in the literature is established. The database is split into randomly selected training and testing sets. To assess the fitting quality, the sum of the absolute difference is used, while maximum depth on trees is set to control the bloat of the model. The performance is assessed with four statistical criteria and three GP models using different input combinations are proposed. These models have been converted into simple mathematical equations to calculate HC based on collected input data. In summary, two out of three models have successfully predicted HC with high correlation to the actual HC (R2 of testing sets ≈ 0.92). Therefore, this study has shown the feasibility of applying GP models into future prediction of HC for the initial phase of rock grouting design.

Design and exploration of low-power SAD architectures using approximate compressors for Integer Motion Estimation

Integer motion estimation performs a pivotal role in achieving video compression by exploiting the temporal redundancy of video sequences. However, the motion estimation’s computational complexity is huge and requires much computational power in real-time. On the other hand, portable mobile devices which operate on battery power have minimal computational capabilities. Since the video encoding can tolerate error up to a specific limit, the hardware complexity can be reduced by approximating the motion estimator’s fundamental modules. The major contributor to the power consumption in the motion estimator is the sum of the absolute difference (SAD) module. This paper presents SAD architectures implemented using new approximate 8:2 compressors to reduce the computational complexity. Thus, leading to a reduction in the hardware complexity and power consumption while maintaining the coding efficiency. Our proposed approximate SAD architecture achieves up to 56.7% and 49.8% savings in power compared to exact compressor-based SAD architectures and existing approximate SAD architectures respectively.

CNN and HEVC Video Coding Features for Static Video Summarization

This study proposes a novel solution for the detection of keyframes for static video summarization. We preprocessed the well-known video datasets by coding them using the HEVC video coding standard. During coding, 64 proposed features were generated from the coder for each frame. Additionally, we converted the original YUVs of the raw videos into RGB images and fed them into pretrained CNN networks for feature extraction. These include GoogleNet, AlexNet, Inception-ResNet-v2, and VGG16. The modified datasets are made publicly available to the research community. Before detecting keyframes in a video, it is important to identify and eliminate duplicate or similar video frames. A subset of the proposed HEVC feature set was used to identify these frames and eliminate them from the video. We also propose an elimination solution based on the sum of the absolute differences between a frame and its motion-compensated predecessor. The proposed solutions are compared with existing works based on an SIFT flow algorithm that uses CNN features. Subsequently, an optional dimensionality reduction based on stepwise regression was applied to the feature vectors prior to detecting key frames. The proposed solution is compared with existing studies that use sparse autoencoders with CNN features for dimensionality reduction. The accuracy of the proposed key-frame detection system was assessed using the positive predictive values, sensitivity, and F-scores. Combining the proposed solution with Multi-CNN features and using a random forest classifier, it was shown that the proposed solution achieved an average F-score of 0.98.

Ultrasound Sub-pixel Motion-tracking Method with Out-of-plane Motion Detection for Precise Vascular Imaging

Ultrasound vascularity imaging provides important information for differential diagnosis of tumors. Peak-hold (PH) is a useful technique for precisely imaging small vessels by selecting a maximum brightness in each pixel through the frames obtained sequentially. To use PH successfully one needs motion compensation to reduce image blur, but out-of-plane motion cannot be avoided. To address this problem, we developed a sub-pixel motion-tracking method with out-of-plane motion detection (OPMD). It is a combination of the sum of the absolute differences (SAD) method and the Kanade-Lucas-Tomasi method and can be accurately applied to various motions. The value from OPMD (γ) is defined as a statistical value obtained from the distribution of residual values in the SAD procedure with the obtained frames. The value is ideally 0, and the frames having large γ are removed from the PH procedure. The accuracy of the proposed tracking method was found by a simulation study to be approximately 20 μm. We also found, through a phantom experiment, that the value of γ sensitively increased enough to detect out-of-plane motion. Most important, γ begins to increase before tracking errors occur. This suggests that OPMD can be used to predict tracking errors and effectively remove frames from the PH procedure. An in vivo experiment with a rabbit showed that the PH image obtained with motion tracking clearly revealed peripheral vessels that were blurred in the PH image obtained without motion tracking. We also found that the image quality becomes better when OPMD was used to remove frames including out-of-plane motion.

Transient Simulation of Natural Gas Network by Hybrid Taguchi Binary Genetic Algorithm

Abstract The analysis of gas transportation networks is the backbone for further processes such as optimization and control. The static analysis is based on algebraic equations which are straightforward and easy to solve, but may result in solutions far from the optimum due to the dynamic nature of the network. Hence, the transient analysis is inevitable. It is based on a set of equations containing partial differential equations (PDEs) for each pipeleg (Navier–Stokes equations), algebraic equations of compressors, the initial conditions and the boundary values. Since the governing equations of each pipeleg are PDEs, the internal boundary values of the network should be considered according to the topography of the pipelegs in the network, which makes the traditional transient analysis complicated and time consuming. In this paper, a straightforward method based on metaheuristic algorithms is proposed for the transient analysis. Using the proposed technique, each pipeleg is analyzed separately which speeds up the analysis. The source flow rates are considered as the optimization variables and based on them, the demand pressures are calculated. The sum of the absolute differences between the real demand pressures (known as the boundary values) and the calculated ones is the error of the proposed modeling. To minimize the error, a powerful metaheuristic algorithm called Hybrid Taguchi Binary Genetic Algorithm is utilized. Numerical results confirm the efficiency and accuracy of the proposed method that leads to near-zero error.

A correlation consistency based multivariate alarm thresholds optimization approach

Different alarm thresholds could generate different alarm data, resulting in different correlations. A new multivariate alarm thresholds optimization methodology based on the correlation consistency between process data and alarm data is proposed in this paper. The interpretative structural modeling is adopted to select the key variables. For the key variables, the correlation coefficients of process data are calculated by the Pearson correlation analysis, while the correlation coefficients of alarm data are calculated by kernel density estimation. To ensure the correlation consistency, the objective function is established as the sum of the absolute differences between these two types of correlations. The optimal thresholds are obtained using particle swarm optimization algorithm. Case study of Tennessee Eastman process is given to demonstrate the effectiveness of proposed method.

Abstract P6-09-04: Volumetric breast density improves breast cancer risk prediction

Abstract Introduction: There is increasing interest in implementing personalized breast cancer screening strategies rather than relying on population based guidelines. Most risk models do not include breast density and two models that do rely on subjective BI-RADS categories; all have limited discriminatory ability (C-statistics ranging from 0.60-0.74). Our aim was to develop a model that includes an automated objective and numeric volumetric measurement of breast density with other known risk factors to improve risk prediction. Methods: A case-control study design was used to evaluate the association between risk factors and breast cancer diagnosis. All women diagnosed with breast cancer during 2003-13 with a digital contralateral mammogram at the University of Virginia at the time of diagnosis were eligible as cases. All women without a breast cancer diagnosis but with a digital mammogram at UVA during 2003-2008 were eligible as controls. Risk factor information was collected using a self-reported electronic questionnaire. Mean automated volumetric breast density (Volpara, NZ) was calculated for each patient as a percentage. Controls were matched to cases in a 2:1 ratio based on age group, race, and education, using the GREEDY algorithm. Case-control selections were made using the weighted sum of the absolute differences between the case and control matching factors. Conditional logistic regression using the partial likelihood function from Cox proportional hazard’s regression was used to fit risk prediction equations to the matched case-control study dataset, with stratification for each case matched set. A full model was estimated including all available covariates for use as a model performance reference standard. A reduced model was then estimated including covariates in the full model that had a Wald Chi-Square/degrees of freedom ratio > 1.0. The performance of the full and reduced models was measured using the C index and the maximum R-Square statistic. Results: The study enrolled 3,445 women; 839 cases and 2,606 controls. Multivariable analysis was conducted using 825 cases and 1,628 controls with 1 or more breast studies reported for the surveyed population. The matching process yielded balanced matching factor values between cases and controls, with no significant differences in age group (p = 0.95), race (p = 0.13), or education (p = 0.86). The full prediction model (with 97 df) yielded a C index of 0.88, and an R-Square of 0.53. The reduced model (with 15 df) had a C index of 0.83 and an R-Square of 0.54. Variables in the reduced model included: mean breast density; biopsy showing ADH, ALH/LCIS; BMI; use of HRT, contraceptives, NSAIDS; smoking; exercise; parity; diabetes; family history of breast cancer, HBOC, Li-Fraumeni, or Cowden Syndromes and/or BRCA mutation. Mean volumetric breast density was a leading independent predictor of case status in both the full (p<0.0001) and reduced models (p=0.0212). Conclusion: Volumetric breast density with other known risk factors may provide more accurate individual risk assessment, enabling clinicians to develop patient centered risk based screening protocols that better inform decision making while including patient preferences. The next steps require independent validation of the risk model in other populations. Citation Format: Jennifer A Harvey, George J Stukenborg, Wendy F Cohn, Kathy L Repich, Olivier Alonzo, Wendy M Novicoff, Martin D Yaffe, William A Knaus. Volumetric breast density improves breast cancer risk prediction [abstract]. In: Proceedings of the Thirty-Seventh Annual CTRC-AACR San Antonio Breast Cancer Symposium: 2014 Dec 9-13; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2015;75(9 Suppl):Abstract nr P6-09-04.

Error concealment algorithm using inter-view correlation for multi-view video

Abstract This paper proposes an error concealment algorithm for whole frame loss for multi-view video decoding. In our proposal, the relationship between motion vectors and disparity vectors is exploited first. Based on the parallelogram-like motion relationship, the motion vectors of error frames can be indirectly derived by projecting the disparity vectors from the counterpart view. In addition, to further improve the concealing results, a joint sum of the absolute difference (SAD) minimization approach is also proposed to find the block for the purpose of concealing the current error block by jointly considering motion vectors and disparity vectors. Experimental results show that our proposed algorithm provides better video quality than previous work and reduces error propagation.

Fast mode decision scheme using sum of the absolute difference‐based Bayesian model for the H.264/AVC video standard

H.264/AVC is the most widely used recent video coding standard. It provides a high encoding efficiency but it also has a high computational complexity. The block mode decision for motion estimation is the most time-consuming procedure. A complexity reduction method for the block mode decision procedure is proposed. To reduce the complexity, all block modes are divided into several candidate block mode groups. The sum of the absolute difference (SAD) value, including the motion cost of each mode, is used as a classification feature to divide the block modes into several groups. A refinement method using a Bayesian model based on the average SAD value is also proposed. For B-slices, a differential block mode allocation method is suggested. A different number of candidate modes are allocated for lists (list 0, list 1) based on the SAD value of each list after 16 × 16 block motion estimation. The proposed method achieves an average time-saving for the total encoding time of 65% for IPPP and 66.01% for the hierarchical-B structure.

Side information generation for frame rate scalable distributed video codecs

A side information (SI) generation method is presented for the distributed video codecs with a scalable frame rate. SI interpolation, based on a hierarchical motion estimation with an adaptive block expansion, is proposed to reduce the power of the virtual channel noise, especially in sequences with lower frame rates. Blocks are classified into subframes in descending order of the estimated sum of the absolute difference (SAD), and each subframe is encoded if the maximum SAD of its blocks is larger than the estimated distortion of the key frames. Through a simulation, the proposed scheme is shown to achieve a coding efficiency close to that of H.264 with a zero motion even for very low frame rates.

A new distortion measure for motion estimation in motion-compensated hybrid video coding

In the video coding standards MPEG-x and H.26x, a motion-compensated prediction technique is used for enhancing the coding performance of bitrate reduction or peak signal to noise ratio (PSNR) improvement. This technique takes advantage of the correlation between consecutive frames in the time domain, which is relatively higher than that between adjacent blocks in the spatial domain. In order to utilize the correlation between consecutive frames, the conventional video coding standards have used the motion estimation (ME) and compensation technique, where the Sum of the Absolute Differences (SAD) is usually used as the distortion measure. The ME estimates the reference block that could minimize the residual signal between the current and reference blocks. However, the SAD is not appropriate to the specific sequences that have global or local illumination changes. In addition, the high-resolution video sequences have higher spatial correlation than the low-resolution video sequences in general. Therefore, a new distortion measure that can consider spatial and temporal correlation simultaneously may be helpful to enhance the coding performance. The proposed distortion measure searches for a reference block that minimizes the motion-compensated residual signal when the DC-component is predicted. In our proposed algorithm, the maximum BD-rate improvement is up to 13.6% for illumination-changed video sequences, and the average BD-rate improvement is 6.6% for various high-resolution video sequences in the baseline profile.

Efficient intra-mode decision algorithm for inter-frames in H.264/AVC video coding

An efficient intra-mode search algorithm is proposed to reduce the computational complexity of inter-frames for the H.264/AVC video encoding system. Each intra-mode search procedure usually causes a high degree of complexity in an inter-frame because of the inter-frame prediction modes that operate with the inter-mode decision procedure. To decrease this computational burden, the authors propose an adaptive thresholding algorithm based on distribution characteristics of the sum of the absolute differences (SAD) of the best inter-mode when the intra-mode is the final coding mode. The authors also include a simple refinement process by using the spatial correlation between neighbouring macro-blocks (MBs) and the current MB. The performance of the proposed algorithm is verified through comparative analysis of encoding time, loss of quality and the bit increment.

Equity-Efficiency Bicriteria Location with Squared Euclidean Distances

A facility must be located within a given region taking two criteria of equity and efficiency into account. Equity is sought by minimizing the inequality in the facility-inhabitant distances, as measured by the sum of the absolute differences between all pairs of squared Euclidean distances from inhabitants to the facility. This measure meets the Pigou-Dalton condition of transfers and can easily be minimized. Efficiency is measured through optimizing the sum of squared inhabitant-facility distances, either to be minimized or maximized for an attracting or repellent facility, respectively. Geometric localization results are obtained for the whole set of Pareto-optimal solutions for each of the two resulting bicriteria problems within a convex polygonal region. A polynomial procedure is developed to obtain the full bicriteria plot, both trade-off curves, and the corresponding efficient sets.

Transforming the exponential by minimizing the sum of the absolute differences

This work presents an optimal value to be used in the power transformation to transform the exponential to normality for statistical process control (SPC) applications. The optimal value is found by minimizing the sum of absolute differences between two distinct cumulative probability functions. Based on this criterion, a numerical search yields a proposed value of 3.5142, so the transformed distribution is well approximated by the normal distribution. Two examples are presented to demonstrate the effectiveness of using the transformation method and its applications in SPC. The transformed data are almost normally distributed and the performance of the individual charts is satisfactory. Compared to charts that use the original exponential data and probability control limits, the individual charts constructed using the transformed distribution are superior in appearance, ease of interpretation and implementation by practitioners.

Estimating the molecular composition of a diverse range of natural organic materials from solid-state 13C NMR and elemental analyses

Most techniques for determining the chemical nature of natural organic matter in soil, sediment and water require prior extraction or concentration steps that are not quantitative and that create artifacts. 13C nuclear magnetic resonance (NMR) analysis can avoid these problems, but it gives little information at the scale of molecules. Here we show that the molecular composition of a diverse range of natural organic materials could be inferred from 13C NMR analysis combined with C and N analysis. Forty-six different organic materials including undecomposed and decomposed plant materials, soil organic matter, phytoplankton, and the organic matter found in freshwater, estuarine and marine sediments were examined. A mixing model simultaneously solved a series of equations to estimate the content of four biomolecule components representing the organic materials produced in greatest abundance by plants and other organisms (carbohydrate, protein, lignin and aliphatic material) and two additional components (char and pure carbonyl). Based on defined molecular structures for each component, signal intensities for 13C NMR spectra were predicted and compared with measured values. The sum of the absolute differences in signal intensity between the measured and predicted spectral regions was <7% for the terrestrial materials. For aquatic materials the fit of the predicted to measured signal intensities was not as good. Predicted molecular compositions correlated well with independent analyses of cellulose, protein and lignin contents of plant samples and char contents of soil samples. Across all samples, carbohydrates accounted for 10-76% of the sample C (40-76% in plants and 10-42% in soils, sediments and phytoplankton), protein for 2-80% (21-80% in phytoplankton and marine water column samples and 2-36% in plants, soils and sediments), lignin for 0-36%, aliphatic materials for 2-44%, char for 0-38% and carbonyl for 0-22%. For the soils, sediments and decomposed plant materials, the close correspondence between actual signal intensities and those predicted using known biomolecular components, suggested that either‘8humic’ structures can be approximated by mixtures of common biologically derived molecules or that humic structures did not exist in significant amounts.

Distance graph on with $ell;1 norm

A long-standing open problem in combinatorial geometry is the chromatic number of the unit-distance graph in R n ; here points are adjacent if their distance in the ℓ 2 norm is 1. For n =2, we know the answer is between 4 and 7. Little is known about other dimensions. The subgraphs induced by the rational points have been studied with limited success in small dimensions. We consider the analogous problem on the n -dimensional integer grid with fixed distance in the ℓ 1 norm. That is, we make two integer grid points adjacent if the sum of the absolute differences in their coordinate values is r . Let the chromatic number of this graph be χ( Z ,r) . The main results of this paper are (i) χ( Z n ,2)=2n for all n , and (ii) (1.139) n ⩽χ( Z n ,r)⩽(1/ 2πn )(5 e ) n for all n and even r . We also give bounds useful for small values of n and r . We also consider the lower and upper bounds on the n -dimensional real space with unit distance under ℓ p norm for 1⩽ p ⩽∞.

All zero macroblock decision method for H.26L

In order to reduce the computation in the part of motion search and transform in H.26L encoder, an all-zero macroblock decision method based on integer transform and motion search is proposed in this paper. According to the characteristics of integer transform and motion search in H.26L, all-zero macroblock decision is made in inter frame coding by comparing Sum of the Absolute Differences(SAD) with a value related with Quantization Parameter(QP) before integer transform. It avoids a large amount of computation in motion search, transform and quantization. This technology highly improves the efficiency of real time H.26L encoder by skipping all-zero macroblock before integer transform and shortening the code stream at the same time.

Distance graph on [formula omitted] with ℓ 1 norm

A long-standing open problem in combinatorial geometry is the chromatic number of the unit-distance graph in R n ; here points are adjacent if their distance in the ℓ 2 norm is 1. For n=2, we know the answer is between 4 and 7. Little is known about other dimensions. The subgraphs induced by the rational points have been studied with limited success in small dimensions. We consider the analogous problem on the n-dimensional integer grid with fixed distance in the ℓ 1 norm. That is, we make two integer grid points adjacent if the sum of the absolute differences in their coordinate values is r. Let the chromatic number of this graph be χ( Z,r) . The main results of this paper are (i) χ( Z n,2)=2n for all n, and (ii) (1.139) n⩽χ( Z n,r)⩽(1/ 2πn )(5 e) n for all n and even r. We also give bounds useful for small values of n and r. We also consider the lower and upper bounds on the n-dimensional real space with unit distance under ℓ p norm for 1⩽ p⩽∞.

Improved multilevel successive elimination algorithm using efficient decision conditions

The computational process of the sum of the absolute difference (SAD) and the multilevel successive elimination algorithm (MSEA) are theoretically analyzed, and a new improved MSEA is proposed. The proposed algorithm reduces the computations required for judging invalid candidate blocks. The simulation results show that the proposed algorithm achieves a computational time savings of about 30 to 40% without additional hardware, compared to the MSEA.