IMAGING SCIENCE GROUP

Members: NG, Michael; LIU, Hongyu; NGAN, Henry; YUAN, Xiaoming; ZENG, Tieyong

Overview: The interdisciplinary field of imaging science is experiencing tremendous growth. New devices capable of imaging objects and structures from nanoscale to the astronomical scale are continuously being developed and improved, and as a result, the research of science and medicine has been extended in exciting and unexpected ways. The impact of this technology has been to generate new challenges asso-ciated with the problems of formation, acquisition, compression, transmission, and analysis of images. By their very nature, these challenges cut across the disciplines of physics, engineering, mathematics, biology, medicine, and statistics. The Imaging Sciences Group works for fundamental results in imaging sciences, with a unique combination of mathematics and applications. The group is mathematically and computationally based, and members study methodology, models, and algorithms among diverse application areas of imaging sciences.

Activities: The group members are a part of the Centre for Mathematical Imaging and Vision (CMIV) at Hong Kong Baptist University (http://www.math.hkbu.edu.hk/ cmiv/). The objectives of the Centre is to pro-mote basic and applied research in mathematical imaging and vision, computational imaging methods and image analysis and recognition, and to provide a research environment for faculty and graduate students with research interests in the aforementioned areas. Faculty members from various departments are involved in the CMIV and the CMIV facilitates their interaction with each other, as well as domestic and interna-tional visitors across universities and the industry. The CMIV is the site for several seminars and conferences for representatives from other universities, including the SIAM Conference on Imaging Sciences, which is the first SIAM Activity Group Meeting to be held in Asia and Hong Kong.

• Color-to-gray is the process to convert a color image to a grayscale one, which is a basic tool in digital printing, photograph rendering and single-channel image processing.

• The main challenge of this research is to preserve as much information from the original color image as possible, and to generate a perceptually plausible greyscale image.

• Our idea is to propose a variational approach containing an energy functional to determine local transformations to combine red, green and blue channels pixel values together by maximizing the local variance of the output grayscale image and preserving the brightness of the input color image. In order to minimize the differences among the local transformations at the nearby pixel locations, the total variation regularization of the transformation is incorporated in the functional for the decolorization process.

• Publication: Z. Jin, F. Li and M. Ng, A Variational Approach for Image Decolorization By Variance Maximization, SIAM Journal on Imaging Sci-ences, V7 (2014), pp. 944-968.

Saddle point problems are fundamental mathematical problems that have been widely studied in a variety of contexts. In this project, we will focus on the convex optimization context and further study the algorithmic design aspects of different saddle point problems. We will integrate several up-to-date techniques developed in the contemporary optimization literature into an algorithmic design study of these problems. A series of new algorithms will be proposed for the different saddle point problems, including such special forms as linearly constrained convex minimiza-tion problems, the canonical minmax problem, and more general problems such as variational inequalities. For each new algorithm, we will rig-orously prove its convergence and estimate its worst-case convergence rate measured by the iteration complexity. We will apply these new al-gorithms to solve modern applications in several areas. The efficiency of the new algorithms will be verified, and insights into their modeling and algorithmic implementation will be gained through this application. Our aim is a better understanding of the algorithmic design aspect of saddle point problems. We expect the project output to strengthen the current research on this important topic.

This proposal of automatic incident classification (AIC) for large-scale traffic data is mainly to contribute to the development of traffic moni-toring and managing for Traffic Control and Surveillance System (TCSS). An effective AIC method enhances the response time to traffic in-cidents and reduces massive human operators in operation. It should be capable to detect and classify a traffic incident from massive data and prevent the result from any corruption of data errors. Over decades, most previous research has mainly focused on the automatic inci-dent detection (AID), with or without incident only. This means no detailed classification of traffic incidents was given. Also, they rarely dealed with data errors embedded on the dataset. Therefore, it is increasing a demand to develop a technology to improve the data quality and strengthen the discriminative power to detect and classify traffic incident. First, it is not straightforward to separate traffic incident and data errors. This proposal offers a new perspective to treat this problem from outlier detection and classification. Outliers are those incon-sistent to the majority of data. Data errors and traffic incidents embedded in traffic datasets are outliers while others are regarded as inliers. Hence, this project will develop the AIC based on a framework of outlier detection and classification method. Second, traffic incident classi-fication requires more advanced techniques and strong support of an accurate traffic incident detection result. Therefore, in this proposal, our AIC would firstly screen outliers (traffic incidents and data errors) and inliers (incident-free events) from massive traffic data by an out-lier detection method with high detection rate. Then, our AIC will perform a finer outlier classification of detected anomalies for 7 outlier types, in which two types belong to data errors and five types belong to traffic incidents. This would contribute to the state-of-the-art TCSS with automatic and accurate traffic incident detection, and fine classification of traffic incidents.

Automatic incident classification for large-scale traffic data(Grant: RGC HKBU12201814, PI: Ngan, Henry)

This project proposes to continue the PI's research on uniqueness, numerical reconstruction algorithms and invisibility cloaking for inverse acoustic and electromagnetic (EM) scattering problems. Inverse scattering problems concern the recovery of unknown/inaccessible objects by acoustic or elec-tromagnetic wave measurements. They are of central importance to many areas of science and technology, including radar and sonar, geophysical ex-ploration, medical imaging, non-destructive testing and remote sensing. However, there are various challenging problems in this field that are far from well understood. Our proposed studies lie in the core of research on inverse scattering problems. For uniqueness, we propose to establish the unique determination of an isotropic acoustic/EM medium by the fixed-incident-direction far-field data. The inverse problems are formally posed with such measurement data. To our best knowledge, there is no such uniqueness result in the literature. The study is based on showing the discreteness of cer-tain acoustic and electromagnetic interior transmission eigenvalues with generic mediums. The uniqueness result would motivate some new inverse scattering modalities. For the numerical reconstruction algorithm, we propose to investigate a novel multiple-shot method, extending the single-shot method developed by the PI and his collaborators in their recent works for inverse scattering problems. The single-shot method makes use of a single far-field measurement, whereas the multiple-shot method would make use of multiple far-field measurements. The extension is highly non-trivial and the proposed method could produce fine reconstructions for some important inverse scattering problems. Particularly, we shall apply the newly devel-oped method to the reconstruction of buried anomalies in a two-layered medium, and to the ground detection with non-flat/rough background ground. Finally, we consider the approximate invisibility cloaking for acoustic and electromagnetic waves. The transformation-optics invisibility cloaking has been widely investigated in the literature in recent years. However, the cloaking mediums obtained via the transformation-optics approach are usually anisotropic. The anisotropy causes sever difficulties for practical realization of the cloaking devices. We shall develop a general framework of con-structing isotropic cloaking devices. The major idea is to investigate the so-called non-scattering potential.

Uniqueness, reconstruction algorithms and invisibility cloaking for inverse scattering problems(Grant: RGC HKBU12302415, PI: Liu, Hongyu)

Further algorithmic study on saddle point problems(Grant: RGC HKBU12300515, PI: Yuan, Xiaoming)

Image decolorizationNg, Michael

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Example: (a) Input color image; (b) the proposed method; (c) global mapping method; (d) Grundland's method.

• We study some computational median filtering methods for extracting static backgrounds from surveillance videos corrupted by noise, blur or both.

• These new methods significantly differ from existing methods originating from the robust principal component analysis (RPCA) in that no nuclear-norm term is involved; thus the computation of singular value decomposition (SVD) can be completely avoided when solving these new models iteratively.

• This is an important feature since usually the dimensionality of a surveillance video is large and so the involved SVD (which is inevitable for RPCA-based models) is very expensive computationally.

• The proposed median filtering based variational models can extract more accurate backgrounds when the background in a surveillance video is static and numerically they can be solved much more efficiently.

• Publication: X. Li, M. Ng and X. Yuan, Median Filtering Based Methods for Static Background Extraction from Surveillance Video, Numerical Linear Algebra with Applications

Median filtering based methods for static background extraction from surveillance videoNg, Michael; Yuan, Xiaoming

Example: Mall Video Frames and the extraction by the proposed method which is four times faster than the RPCA method.

Variational models in image segmentation: Theoretical issues and applications (Grant: RGC HKBU12302714, PI: Zeng, Tieyong)Image segmentation is a central problem in image processing applications, which aims to distinguish objects in an image foreground from the background and to systematically select specific features from an image that has many features. This research proposal involves the develop-ment of image segmentation models from variational approaches, with particular efforts on real applications. Previously, there have been many segmentation algorithms designed under different conditions, mostly multiphase segmentation algorithms that are very complex and based on very strict conditions. In this project, the variational approaches will be based on the theory of image segmentation, image restora-tion, optimization and statistics to handle image segmentation. As in our previous research on image processing, we will concentrate on sev-eral aspects --- viz. efficient algorithms considering blurring effects, an extension to non-Gaussian noise, segmentation of the images with in-tensity inhomogeneity, motion segmentation, and selective segmentation. These are considered to represent the most important issues re-quiring substantial research for image segmentation problems. Apart from its academic interest, this research proposal will apply to important real-life applications such as medical imaging, biological imaging and Synthetic Aperture Radar imagery.

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Segmentation comparison: (a) given image, (b) FRC, (c) SW-Potts, (d) smooth solution, (e) our method.

(c) (d) (e)

Research Interests: • Image Processing, including denoising, deblurring, decomposition, reconstruction and segmen-

tation.• Inverse Problems, including compressive sensing, inverse scattering and super-resolution.• Data Analysis, including social signal processing, visual surveillance, classification and learning,

high-dimensional data mining, and network analysis.• Applications, including computational photography, medical imaging and astronomical imaging.