editorial mathematical methods applied to digital image processing · 2019. 7. 31. · images, and...

EditorialMathematical Methods Applied to Digital Image Processing

Yi-Hung Liu,1 Chung-Hao Chen,2 and Paul C.-P. Chao3

1 Department of Mechanical Engineering, Chung Yuan Christian University, Chungli 32023, Taiwan2Department of Electrical and Computer Engineering, Old Dominion University, Norfolk, VA 23529, USA3Department of Electrical Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan

Correspondence should be addressed to Yi-Hung Liu; [email protected]

Received 5 March 2014; Accepted 5 March 2014; Published 22 April 2014

Copyright © 2014 Yi-Hung Liu et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Digital image processing (DIP) is an important research areasince it spans a variety of applications. Although over thepast few decades there has been a rapid rise in this field,there still remain issues to address. Examples include imagecoding, image restoration, 3D image processing, featureextraction and analysis, moving object detection, and facerecognition. To deal with these issues, the use of sophisticatedand robust mathematical algorithms plays a crucial role.The aim of this special issue is to provide an opportunityfor researchers to publish their latest theoretical and tech-nological achievements in mathematical methods and theirvarious applications related to DIP. This special issue coverstopics related to the development of mathematical methodsand their applications. It has a total of twenty-four high-quality papers covering various important topics in DIP,including image preprocessing, image encoding/decoding,stereo image reconstruction, dimensionality and data sizereduction, and applications.

2. Image Preprocessing

One of the topics covered in this special issue is related tothe image preprocessing methods, including segmentation,thresholding, denoising, image interpolation, calibration ofcameras, and image restoration. There are twelve papersrelated to this topic, occupying half of the papers included inthis special issue. The paper entitled “An improved adaptivedeconvolution algorithm for single image deblurring” by H.-C. Tsai and J.-L. Wu proposes an adaptive regularization

method, which can preserve image details and suppressringing artifacts simultaneously. Their results carried out onsynthesized and real images show that their method canrestore latent image with much fewer ringing and favors thesharp edges. S. Pan et al. propose the paper entitled “OptimalO(1) bilateral filter with arbitrary spatial and range kernelsusing sparse approximation.” In this paper, an approximatingarbitrary spatial kernel using a fixed number of boxes ispresented. The multiple-box spatial kernel can be applied inmanyO(1) acceleration schemes in addition to the histogram-based one. Their results show that the proposed methodhas better accuracy in approximating the bilateral filter withGaussian spatial kernel, compared with previous histogram-based methods.

Then, the paper titled “Fast total-variation image decon-volution with adaptive parameter estimation via split Bregmanmethod” by C. He et al. studies how to balance the total-variation (TV) regularization and data fidelity, which hasconsidered a challenging issue in image restoration. Theirproposedmethod extends the classical split Bregmanmethodto a new fast algorithm, which simultaneously estimates theregularization parameter and restores the blurred image.Theregularization parameter is refreshed conveniently in a closedform according to Morozov’s discrepancy principle. Anotherpaper of this topic is “Robust calibration of cameras withtelephoto lens using regularized least squares” byM. Liang et al.This paper has two main contributions. First, they present afirst-order error analysis that shows the relation between focallength and estimation uncertainties of camera parameters.To our knowledge, this error analysis with respect to focallength has not been studied in the area of camera calibration.

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014, Article ID 480523, 4 pageshttp://dx.doi.org/10.1155/2014/480523

2 Mathematical Problems in Engineering

Second, they propose a robust algorithm to calibrate thecamera with a long focal length without using additionaldevices: the covariance of camera parameters can be reducedgreatly.

The next paper of this topic is “A block-based regularizedapproach for image interpolation” by L. Chen et al. This paperstudies how to render a high-resolution image from a low-resolution image. Classical interpolation techniques estimatethe missing pixels from the surrounding pixels based on apixel-by-pixel basis. In contrast, this paper presents a newefficient algorithm for image interpolation based on regular-ization theory, which formulates the interpolation problem asan optimization problem in which the cost function consistsof a data fidelity term and regularization functional. Thecomputational cost of this algorithm is further reduced byincorporating Kronecker product and singular value decom-position. The effect of regularization on the interpolationresults is analyzed in this paper. Next, the paper entitled “Sen-sor selection and integration to improve video segmentationin complex environments” coauthored by A. R. Reckley et al.proposes a technique to integrate spatiotemporal signaturesof an object of interest from different sensing modalitiesinto a video segmentation method in order to improveobject detection and tracking in dynamic, complex scenes.Their proposed algorithm utilizes the dynamic interactioninformation between the object of interest and background todifferentiate betweenmistakenly segmented components andthe desired component. S. Tehsin et al. proposed the paperentitled “Fuzzy-based segmentation for variable font-sized textextraction from images/videos,” which addresses the issue oftext localization and detection by using a novel fuzzy-basedsegmentation method.

Moreover, Poissonian image deconvolution is a key issuein various applications, such as astronomical imaging, med-ical imaging, and electronic microscope imaging. To addressthis issue, Y. Shi et al. propose the paper “Poissonian imagedeconvolution via sparse and redundant representations andframelet regularization”. In this paper, an approach that com-bines analysis with synthesis methods is proposed. The aimis to address the Poissonian image deconvolution problem byminimizing an energy functional.Theminimization problemcan be efficiently solved by the split Bregman technique. D.-X.Xia et al. propose the paper entitled “Fast threshold selectionalgorithm of infrared human images based on two-dimensionalfuzzy Tsallis entropy.” In this paper, a fast thresholdingmethod of infrared human images based on two-dimensionalfuzzy Tsallis entropy is introduced. First, to address thefuzziness of infrared image, the fuzzy Tsallis entropy ofobjects and that of background are defined, respectively,according to probability partition principle. Next, this newlydefined entropy is extended to two dimensions to make gooduse of spatial information to deal with the noise in infraredimages, and correspondingly a fast computation methodof two-dimensional fuzzy Tsallis entropy is put forward toreduce its computation complexity.

Another paper to this set is “Image denoising using totalvariation model guided by steerable filter” by W. Zhang et al.This paper proposes an adaptive total variation (TV) modelby introducing the steerable filter into the TV-based diffusion

process for image filtering. The proposed model can providea better image processing tool which enables noise removal,edge-preserving, and staircase suppression. The paper alsothat belongs to this topic is the one entitled “A globalmultilevel thresholding using differential evolution approach”by K. Charansiriphaisan et al. The optimal Otsu thresholdvalues of multilevel image thresholding are necessary forsome applications and a global search algorithm is required.Previously, differential evolution (DE) algorithm has beenused successfully for solving this problem. However, the dif-ficulty of problem grows exponentially when the number ofthresholds increases. To overcome this difficulty, an improvedDEusing newmutation strategy is proposed in this paper.Thelast paper of this topic is related to image restoration.W.Qidi,et al. propose the paper entitled “The nonlocal sparse recon-struction algorithm by similarity measurement with Shearletfeature vector,” which supplies a nonlocal sparsity reconstruc-tion algorithm with similarity measurement to improve theaccuracy of conventional methods of image restoration. Toimprove the performance of restoration results, this paperproposes two schemes to dictionary learning and sparsecoding, respectively. In the part of the dictionary learning,the similarity between patches from degraded image byconstructing the Shearlet feature vector is measured. In thepart of sparse coding, an optimal objective function with thecoding residual item is performed, which can suppress theresidual between the estimate coding and true sparse coding.The derivation of self-adaptive regularization parameter inoptimization under the Bayesian framework is also provided,which can make the performance better.

3. Stereo Image Reconstruction

In this special issue, there are three papers related to the topicof stereo image reconstruction. The homography betweenimage pairs is normally estimated by minimizing a suitablecost function, given a set of 2D keypoint correspondences.The correspondences are typically established using descrip-tor distance of keypoints. However, the correspondences areoften incorrect due to ambiguous descriptors which canintroduce errors into following homography computing step.There have been numerous attempts to filter out these erro-neous correspondences, but it is unlikely to always achieveperfect matching. To deal with this problem, W. Mou et al.propose the paper entitled “Robust homography estimationbased on nonlinear least squares optimization,” in which anonlinear least squares optimization approach is presented tocompute homography such that falsematches have no or littleeffect on computed homography.

Moreover, developing matching algorithms from stereoimage pairs to obtain correct disparity maps for 3D recon-struction has also been the focus of intensive research. Aconstant computational complexity algorithm to calculatedissimilarity aggregation in assessing disparity based onseparable successive weighted summation (SWS) amonghorizontal and vertical directions was proposed but still notsatisfactory. To address this issue, C.-T. Zhu et al. proposethe paper entitled “Efficient stereo matching with decoupled

Mathematical Problems in Engineering 3

dissimilarity measure using successive weighted summation,”which presents a novel method enabling decoupled dis-similarity measure in the aggregation, further improvingthe accuracy and robustness of stereo correspondence. Theaggregated cost is also used to refine disparities based on alocal curve-fitting procedure.

Then, the paper entitled “Rendering distortion estimationmodel for 3D high efficiency depth coding” by Q. Zhang etal. proposes a modified distortion estimation model basedon view rendering distortion. This model can be applied tothe high efficiency video coding (HEVC) rate distortion costfunction process for rendering view quality optimization.Their experimental results on various 3D video sequencesshow that this model can provide about 31% BD-rate savingsin comparison with HEVC simulcast and 1.3 dB BD-PSNRcoding gain for the rendered view.

4. Image Encoding and Decoding

Two papers published in this special issue are focusedon image encoding and decoding. The paper entitled “2Dbarcode image decoding” coauthored by J.-A. Lin and C.-S. Fuh studies how to decode various quick response (QR)code images efficiently and accurately. This paper revisesthe traditional decoding procedure by proposing a serialof carefully designed preprocessing methods. The decodingprocedure consists of image binarization, QR code extrac-tion, perspective transformation and resampling, and errorcorrection. By these steps, different types of QR code imagescan be recognized accurately. K. T. Lin and S. L. Yehpropose the paper entitled “Hiding a covert digital image byassembling the RSA encryption method and the binary encod-ing method,” which integrates the Rivest-Shamir-Adlemanencryption method and the binary encoding method to forma hybrid hiding method that can hide a covert digital imageinto a dot-matrix holographic image. The pixels of the dot-matrix holographic image contain seven groups of codes usedfor reconstructing the covert image, and the reconstructedcovert image derived from the dot-matrix holographic imageand the original covert image are exactly the same.

5. Dimensionality and Dataset Size Reduction

There are two papers in this topic. In image recognition,feature extraction plays a critical role. Feature extractiontypically suffers from the problem of high dimensionality.Therefore, the issue of dimension reduction is of primaryimportance. The convex nonnegative matrix factorization(CNMF) is a variation of nonnegative matrix factorization(NMF) in which each cluster is expressed by a linear com-bination of the data points and each data point is representedby a linear combination of the cluster centers. When thereexists nonlinearity in the manifold structure, both NMFand CNMF are incapable of characterizing the geometricstructure of the data. The paper “Neighborhood preservingconvex nonnegative matrix factorization” by J. Wei et al.introduces a neighborhood preserving convex nonnegative

matrix factorization (NPCNMF), which imposes an addi-tional constraint on CNMF that each data point can berepresented as a linear combination of its neighbors. Thismethod is able to reap the benefits of both nonnegativedata factorization and the purpose of manifold structure.The feasibility and effectiveness of NPCNMF are verified onseveral standard data sets with promising results.

Another major problem of pattern recognition systemsis due to the large volume of training datasets includingduplicate and similar training samples. As a result, a largememory is required for saving data, as well as the hightime complexity for training the algorithms. The paperentitled “Anew dataset size reduction approach for PCA-basedclassification in OCR application” by M. A. Shayegan and S.Aghabozorgi reports on the use of a version of the ModifiedFrequency Diagram technique for dataset size reduction.In this new proposed technique, a big training dataset isrearranged and then sieved.The sieved training dataset alongwith automatic feature extraction/selection operation usingPrincipal Component Analysis (PCA) is used in an opticalcharacter recognition (OCR) application. The experimentalresults obtained when using the proposed system on one ofthe biggest handwritten Arabic/Farsi numeral standard OCRdatasets, Hoda, show about 97% accuracy in the recognitionrate.The recognition speed increased by 2.28 times, while theaccuracy decreased only by 0.7%.

6. Applications

In this special issue, five papers are related to DIP applica-tions. Among the five papers, three are directly related toface detection and recognition. Y.-H. Liu et al. propose thepaper entitled “A support vector data description committeefor face detection,” which develops a one-class learning-basedface detector called support vector data description (SVDD)committee, which consists of several SVDDmembers, each ofwhich is trained on a subset of face patterns. Since nonfacesare not required in the training of the SVDD committee, facedetection accuracy of SVDD committee is independent of thenonface training patterns. Experiments carried out on theextended MIT face dataset show that the proposed SVDDcommittee can achieve better face detection accuracy thanthe widely used SVM face detector. Z. Jian et al. propose thepaper entitled “A fast iterative pursuit algorithm in robust facerecognition based on sparse representation.” In this paper, arelatively fast pursuit algorithm for face recognition is pro-posed.The recognition rates on ORL database, Yale database,and FERET database are 95.5%, 93.87%, and 92.29%, respec-tively. The recognition performance under various levels ofocclusion and corruption is also experimentally proved tobe significantly enhanced. The paper “An improved metriclearning approach for degraded face recognition” by G. Zouet al. also addresses the face recognition problem. To solvethe matching problem of the elements in different datacollections, an improved coupled metric learning approachis proposed in this paper. Experiments based on Yale andCAS-PEAL-R1 face databases demonstrate that the proposedkernel coupled approach performs better in low-resolution

4 Mathematical Problems in Engineering

and fuzzy face recognition and can reduce the computingtime.

In addition to face recognition, other problems arealso challenging in real-word applications. J. Xiang et al.propose the paper entitled “Moving object detection andshadow removing under changing illumination condition” thataddresses the problem of moving object segmentation byproposing a local intensity ratio model that is robust toillumination change. Y. H. Liu et al. propose the paper enti-tled “Low-resolution tactile image recognition for automatedrobotic assembly using kernel PCA-based feature fusion andmultiple kernel learning-based support vectormachine.” In thispaper, a robust tactile sensing image recognition scheme isproposed, a kernel PCA feature fusion layer is performedto extract distinguishing features from a set of candidatefeatures including Fourier descriptors and geometric features,and a multiple kernel learning support vector machine isused as the classifier. The proposed recognition scheme isable to achieve a high recognition rate of over 85% for theclassification of 12 commonly used metal parts in industrialapplications.

Acknowledgments

The guest editors would like to thank the authors andreviewers of the journal who worked on the publication ofthis special issue.

Yi-Hung LiuChung-Hao ChenPaul C.-P. Chao

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