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Posters: Fixed-point algorithm based on proximity operator for image denoising Yizun LIN Abstract: ROF total-variation model is one of the most popular models for image processing. In the model, the denoised image is the proximity operator of the total- variation evaluated at a given noisy image. The total-variation can be viewed as the composition of a convex function (the 1-norm for the anisotropic total-variation or the 2-norm for the isotropic total-variation) with the fist-order difference operator. In order to solve the minimization problem of the ROF total-variation model, we introduce some definitions such as subdifferential and proximity operator, then prove many theorems and lemmas about them. In addition, we provide a characterization in respect to the subdifferential and proximity operator of convex functions. This characterization plays a crucial role in the development of our algorithm to slove the ROF model. We then investigate the proximity operator of the composition of a convex function with a linear transformation. Consider that the operator of 1-norm and 2- norm is easy to be solved, we can use the characterization about the subdifferential and proximity operator as well as the chain rule of subdifferential to transform the problem about the proximity operator of the composition of a convex function with a linear transformation into a fixed-point problem. Since the operator which we want to compute its fixed-point is nonexpansive, we can get the convergence of the Picard iterations. Specialize the fixed-point methodology to the total-variation model, we finally develop our fixed-point algorithm based on the proximity operator. Key wordtotal-variation, subdifferential, proximity operator, fixed-point

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Page 1: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

Posters:

Fixed-point algorithm based on proximity operator for image denoising

Yizun LIN

Abstract:

ROF total-variation model is one of the most popular models for image

processing. In the model, the denoised image is the proximity operator of the total-

variation evaluated at a given noisy image. The total-variation can be viewed as the

composition of a convex function (the 1-norm for the anisotropic total-variation or

the 2-norm for the isotropic total-variation) with the fist-order difference operator.

In order to solve the minimization problem of the ROF total-variation model, we

introduce some definitions such as subdifferential and proximity operator, then

prove many theorems and lemmas about them. In addition, we provide a

characterization in respect to the subdifferential and proximity operator of convex

functions. This characterization plays a crucial role in the development of our

algorithm to slove the ROF model.

We then investigate the proximity operator of the composition of a convex

function with a linear transformation. Consider that the operator of 1-norm and 2-

norm is easy to be solved, we can use the characterization about the subdifferential

and proximity operator as well as the chain rule of subdifferential to transform the

problem about the proximity operator of the composition of a convex function with a

linear transformation into a fixed-point problem. Since the operator which we want

to compute its fixed-point is nonexpansive, we can get the convergence of the Picard

iterations. Specialize the fixed-point methodology to the total-variation model, we

finally develop our fixed-point algorithm based on the proximity operator.

Key word:total-variation, subdifferential, proximity operator, fixed-point

Page 2: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

An idea to improve the result of ROF model by sharpen kernel

convolution

Hao LIU

Abstract:

When an image is corrupted by Gaussian noise with large standard deviation, it

is hard to get good result by only adopting ROF model to recover it. We introduce an

idea to improve the result by using ROF model and sharpen kernel convolution

together. We can get some improvement in the result and a higher PSNR value.?

Linearized alternating direction method for a convex model of

materialidentification in hyperspectral image

Yoko OKUDA

Abstract:

Hyperspectral imaging sensors record up to several hundred

differentfrequencies and hyperspectral image is used for material identification.

Material identification in hyperspectral image is mathematically solved as a non-

negative matrix factorization. In 2011, a new model to solve this problem as a convex

optimization is proposed by E. Esser et al. This model is solved by alternating

direction method of multipliers (ADMM). In 2011, linearized alternating direction

method (ADM) is proposed by R. Chan et al. and this method reduces computation

cost. We apply linearized ADM to the model of this problem to reduce its

computation cost. In this talk, the model of this problem from non-negative matrix

factorization to convex optimization and the difference of experimental results

between solving by ADMM and linearized ADM are discussed.

Page 3: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

Determination of regularization parameter in estimation of the Robin

coefficient in the Laplace equation

Chao WANG

Abstract:

We consider the inverse problem of determining the Robin coefficient by using

measuring data from the accessible part of the boundary, which is nonlinear and ill-

posed. Two regularization methods, namely, the Tikhonov regularization and the H1

regularization, are considered. We propose a Gauss-Newton method to solve the

regularized nonlinear least square problem and a way to choose a suitable

regularization parameter based on the normalized cumulative periodogram.

Numerical results show that these methods are efficient and competitive.

Lax-Friedrichs fast sweeping method for solving eikonal equations on

surfaces

Ka-Wah WONG

Abstract:

Eikonal equation has many applications in computer vision, optimal control and

other areas. There are plenty nice methods for solving eikonal equations on

rectangular grids but there are relatively few for solving it on the surfaces. In here,

we propose a simple surface eikonal solver which is found to be both moderately

accurate and computational efficient.

Page 4: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

A Recursive Algorithm for Multi-frequency Acoustic Inverse Source

Problems.

Boxi XU

Abstract:

We investigate an iterative/recursive algorithm for recovering unknownsources

of acoustic field with multi-frequency measurement data. Under some additional

regularity assumptions on the source functions, rigorous convergence analysis is

presented assuming the background medium is homogeneous and the measurement

data is noise-free. Error bound estimate is also provided when the observation data

is contaminated by some noise. Numerical illustrations verify the reliability and

efficiency of our proposed algorithm.

Patch-based Inpainting Using Adaptive Dictionary by ADMM

Yu YANG

Abstract:

Image inpainting desires to fill in the data in missing area using the information

from the observed region of an image. In this work, we introduce a novel patch-

based inpainting model and algorithm using adaptive dictionary under alternating

direction method of multipliers (ADMM) optimization framework. The optimization

model for linear combination coefficients of similar patches is regularized by `2 norm

and is efficient solved by proposed ADMM-based algorithm. A metric measuring

similarity between two patches is proposed by Laplace probability distribution of

coefficients of DCT tight frame system and is more robust to distinguish difference of

patch than sum of squared differences by `2 norm. The patch-based dictionary can

be adaptively established by proposed metric from the nonlocal data and is similar to

target patch. Inpainting processing order of each patch is determined by improved

patch sparsity. The results show that the proposed patch-based image inpainting

algorithm is efficient in interpolating large missing region and provides more

plausible from the points of visual effect.

Page 5: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

The Regularization Parameter

Meipeng ZHI

Abstract:

There are three parameters of the proximity algorithm. We discuss how to

choose these parameters in order to make the algorithm become more efficient.

Moreover, the most important is the regularization parameter. The choice of this

parameter effects the balance between removing the noise and preserving the signal

content. We introduce the relationship between the regularization parameter and

the ROF model. Finally, we try to propose a new method to solve the ROF model.

Page 6: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

Oral Presentation

A Convex Variational Model for Restoring Blurred Images with Rician

Noise.

Liyuan CHEN

Abstract:

In this presentation, a new convex variational model for restoring images

degraded by blur and Rician noise is proposed. The new method is inspired by

previous works in which the non-convex variational model obtained by maximum a

posteriori (MAP) estimation has been presented. Based on the statistical property of

Rician noise, we put forward to adding an additional data-fidelity term into the non-

convex model, which leads to a new strictly convex model under mild condition. Due

to the convexity, the solution of the new model is unique and independent of the

initialization of the algorithm. We utilize a primal-dual algorithm to solve the model.

Numerical results are presented in the end to demonstrate that with respect to

image restoration capability and CPU-time consumption, our model outperforms

some of the state-of-the-art models in both medical and natural images.

Page 7: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

A novel cell nuclei segmentation method for 3D C. elegans embryonic

time-lapse images

Long CHEN

Abstract:

Recently a series of algorithms have been developed, providing automatic tools

for tracing C. elegans embryonic cell lineage. In these algorithms, 3D images

collected from a confocal laser scanning microscope were processed, the output of

which is cell lineage with cell division history and cell positions with time. However,

current image segmentation algorithms suffer from high error rate especially after

350-cell stage because of low signal-noise ratio as well as low resolution along the Z

axis (0.5-1 microns). As a result, correction of the errors becomes a huge burden. So

we proposed a new type of nuclei segmentation method embracing an bi-directional

prediction procedure, which can greatly reduce the number of false negative errors,

the most common errors in the previous segmentation. The result of this research

demonstrates the advantages of the bi-directional prediction method in the nuclei

segmentation over that of existing method (StarryNite/MatLab StarryNite). Our

method could be an efficient tool for the analysis of high-throughput large C. elegans

microscopy image data sets.

Page 8: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

Optimized Conformal Parameterization with Controllable Area

Distortions

Ka Chun LAM

Abstract:

Parameterization, a process of mapping a complicated domain onto a simple

parameter domain, is important in various fields such as computer graphics, medical

imaging and numerical computation. Conformal parameterization has been widely

used since it preserves the local geometry well. However, a major drawback is that

conformal parameterization often introduces area distortions, which leads to

problems in some applications such as texture mapping. It is therefore desirable to

obtain a parameterization that balances between conformality and area distortions.

In this work, we propose a variational algorithm to compute the optimized conformal

parameterization with controllable area distortions. The distribution of area

distortions can be prescribed by users according to the applications. The main idea is

to minimize a combined energy functional involving the Beltrami coefficient and

Jacobian terms, which are used to control the conformality and area distortions

respectiviely. Soft or hard landmark constraints can also be incorporated into the

model. Experiments have been carried out on real surface data. Results demonstrate

the efficacy of the proposed model to obtain an optimized parameterization that

preserves both local geometry and area distortion as good as possible.

Page 9: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

Comparison of 3 algorithms for computation of Teichmuller extremal

maps

Tsz Chun YAM

Abstract:

Conformal maps, which are angle preserving diffeomorphisms, have been

widely applied in geometry processing, such as surface registration, texture mapping

and remeshing. However, when landmark constraints between the surfaces are

imposed, obtaining conformal map may not be faesible. In this case, quasi-conformal

maps, which allow controlled conformal distortion, will be considered instead.

Several schemes have been proposed for computation of quasi-conformal maps by

minimizing certain type of energy. Lipman et al. proposed a concept of bounded

distortion space and minimize the energy functional in its convex partition by

Quadratic programming or conic programming. Weber et al. and Lui et al. proposed

some computation schemes of a special kind of quasi-conformal maps, called

Teichmuller extremal maps, in a completely different manner. In this presentation,

we will briefly introduce their mathematical models and compare their performance

in different experiments.

Page 10: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

A new fruit recognition method based on multiple features fusion

Hulin KUANG

Abstract:

Fruit recognition, a technique which automatically recognizes classes of fruits in

an image, has widely applications in automating fruit harvest machine, supermarket

and grocery store, children education and health monitoring system in mobile phone.

In this presentation, a new fruit recognition method based on multiple features

fusion is present. A large and complex fruit dataset which contains 20 classes of fruit

is built. Five features including simple shape, color, Local Binary Pattern (LBP),

Histogram of Oriented Gradients (HOG) and LBP feature based on magnitude of

Gabor feature (named GaborLBP) are combined. The five features are complement

with each other. An optimal feature parameters and multiple feature fusion

selection framework is utilized. The optimal feature parameters are selected by

learning and cross validation on the training samples. The optimal multiple features

fusion is selected by fruit recognition accuracy. In addition, machine learning

algorithm also influences the recognition accuracy. Therefore, four machine learning

algorithms including Support Vector Machine (SVM), Multi-class Adaboost, Artificial

Neural Network (ANN) and K nearest neighbors (KNN) are tested to select the

optimal combination of feature fusion and machine learning algorithm. When our

method is compared with other fruit recognition algorithms using the same dataset,

it is demonstrated that our proposed method achieves the highest classification

accuracy at 89.4% for 20 classes of fruits.

Page 11: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

Detecting Alzheimer Disease Patients' Brain Structures with Quasi-

conformal Method.

Hanfang LI

Abstract:

In my presentation, I mainly focus on using the quasi-conformal method in

comparing the brain structures between normal people and Alzheimer Disease

patients. This method can be highly accurate and time-saving when doing the

analysis. We use the MRI scans of many patients in doing surface reconstructions. By

finding out the structure difference among patients, we can assist the neuro-

scientists in observing the main atrophic structure and thus can further develop

some cure methods in dealing with this disease.

Effective noise–suppressed and artifact-reduced reconstruction of

SPECT data using a preconditioned alternating projection algorithm

Si LI

Abstract:

We have recently developed a Preconditioned Alternating Projection Algorithm

(PAPA) with total variation (TV) regularizer for solving the penalized maximum

likelihood optimization model for SPECT reconstruction. This algorithm belongs to a

novel class of fixed-point proximity methods. The goal of this work is to investigate

how PAPA performs while dealing with realistic noisy SPECT data, to compare its

performance with more conventional algorithms, and to address issues with TV

artifacts by proposing a novel form of the algorithm invoking high-order (HO) TV

regularization, denoted as PAPA-HOTV. For high-noise simulated SPECT data, PAPA-

HOTV significantly outperforms several conventional methods in terms of “hot”

lesion detectability, noise suppression, and computational efficiency, with only

limited loss of local spatial resolution. Unlike TV-type methods, PAPA-HOTV does not

create sizable staircase artifacts. PAPA-HOTV shows significant promise for clinically

useful reconstructions of low-dose SPECT data. Therefore, it offers an approach to

the important need of reducing radiation dose to patients in selected nuclear

medicine studies.

Page 12: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

Color Image Segmentation by Minimal Surface Smoothing

Zhi LI

Abstract:

In this paper, we propose a two-stage approach for color image segmentation,

which is inspired by minimal surface smoothing. Indeed, the first stage is to find a

smooth solution to a convex variational model related to minimal surface smoothing.

The classical primal-dual algorithm can be applied to efficiently solve the

minimization problem. Once the smoothed image $u$ is obtained, in the second

stage, the segmentation is done by thresholding. Here, instead of using the classical

K-means to find the thresholds, we propose a hill-climbing procedure to find the

peaks on the histogram of $u$, which can be used to determine the required

thresholds. The benefit of such approach is that it is more stable and can find the

number of segments automatically. Finally, the experiment results illustrate that the

proposed algorithm is very robust to noise and exhibits superior performance for

color image segmentation.

Brief introduction to fMRI

Hongwu LIN

Abstract:

We use our brains everyday but know only a little about them. FMRI providesus

a powerful tool to investigate into our brains. A short introduction of brain and fMRI

are given first in section 1, then some mature mathematical methods and a mixed

model in section 2.

Page 13: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

High Resolution Image Deblurring with Displacement Errors by using

envl1/TV Model

Wenting LONG

Abstract:

High resolution image reconstruction arises in many applications, such as re-

mote sensing, surveillance, and medical imaging. It refers to the reconstruc- tion of

high-resolution image from multiple low-resolution, shifted, degraded samples of a

true image. Displacement error is inevitable during the capture of low resolution

image. The goal for this work is to address the specific issue of high resolution image

reconstruction with displacement error by propos- ing a novel model invoking the

Moreau envelop, denoted by envl1 /TV, which has been studied and explored

extensively in the present work, to compare its performance with classic L2-TV

deblurring model while dealing with realistic noisy data by proposing a fixed point

algorithm, whose convergence condition has been given in the meantime, and a

adaptive stratedy has been given for better PSNR appearance and faster convergence

rate. Two metrics have been carefully selected to quantify the simulation result

which are often used in medical image processing, and it shows that envl1 /TV model

is more effective in noise-suppressed and artifact-reduced.

Page 14: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

Fast Video Compression Algorithms and Real-Time encoder

implementations

Biao MIN

Abstract:

To satisfy the demands of transmission and storage of HD (High Definition) and

UHD (Ultra High Definition) videos, a lot of video compression techniques have been

proposed in recent decades, and the standardized video compression frameworks

are widely applied in various fields. HEVC (High Efficient Video Coding) standard,

released in 2013, is considered to be highly progressive in coding efficiency. The

advanced novelties include quad-tree based block partitioning, refined intra

prediction angles, advanced motion vector prediction, fractional samples

interpolation, block merging, in-loop de-block filtering and adaptive offset. Under the

equal perceptual quality, these new techniques can reduce 40%~50% bitrate over

previous standards and other proposals, while the encoder is also expected to be

several times more complex.

This talk gives some fast algorithms that can be embedded into HEVC

framework to reduce the coding complexity, while the coding efficiency is retained.

The proposed methodologies include fast algorithms for intra prediction and inter

prediction in HEVC. The fast intra prediction algorithm is based on the proposed edge

complexity, and the fast inter algorithm uses the motion information of spatial and

temporal neighbors as reference. In this talk, the hardware architecture is also

presented to discuss how the encoder can be implemented efficiently on hardware

platforms.

Page 15: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

Image reconstruction under non-Gaussian noise

Federica SCIACCHITAO

Abstract:

Digital images are often subject to a variety of distortions during the acquisition,

processing, compression, storage, transmission and reproduction. One of the most

important task of mathematical image processing is to reconstruct the original image

from the blurred and degraded image. During the years, the additive white Gaussian

noise has been widely studied, since it is the most simple and tractable noise.

However, since Gaussian noise does not exist in the real application, other kinds of

noise have been introduced. In this talk, we focus on the impulse and Cauchy noise.

Based on total variation, we propose two variational methods for recovering blurred

images corrupted with impulse noise and Cauchy noise. Numerical results show the

potential of the proposed methods comparing with the existing methods.

Page 16: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

Quasi-conformal parameterizations for multiply-connected domains

Kin Tat HO

Abstract:

In this talk, I am going to present a method to compute the Quasi-conformal

parameterization (QCMC) for a multiply-connected 2D domain or surface. QCMC

computes a Quasi-conformal map from a multiply-connected domain S onto a

punctured disk Ds associated with a given Beltrami differential. The Beltrami

differential, which measures the conformality distortion, is a complex-valued

function with supremum norm strictly less than 1. Every Beltrami differential gives

a conformal structure of S. Hence, the conformal module of Ds, which are the radii

and centers of the inner circles, can be fully determined by, up to a Möbius

transformation. In our project, we proposed an iterative algorithm to simultaneously

search for the conformal module and the optimal Quasi-conformal parameterization.

The key idea is to minimize the Beltrami energy subject to a suitable boundary

constraints. The optimal solution is our desired Quasi-conformal parameterization

onto a punctured disk. The parameterization of the multiply-connected domain

simplifies numerical computations and has important applications in various fields,

such as in computer graphics and vision. Experiments have been carried out on

synthetic data together with real multiply-connected Riemann surfaces. Results show

that our proposed method can efficiently compute Quasi-conformal

parameterizations of multiply-connected domains and outperforms other state-of-

the-art algorithms. Applications of the proposed parameterization technique have

also been explored.

Page 17: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

FLASH: Fast Landmark Aligned Spherical Harmonic Parameterization for

Genus-0 Closed Brain Surfaces

Pui Tung CHOI

Abstract:

Surface registration between cortical surfaces is crucial in medical imaging for

performing systematic comparisons between brains. Landmark-matching registration

that matches anatomical features, called the sulcal landmarks, is often required, to

obtain a meaningful 1-1 correspondence between brain surfaces. This is commonly

done by parameterizing the surface onto a simple parameter domain, such as the

unit sphere, in which the sulcal landmarks are consistently aligned. Landmark-

matching surface registration can then be obtained from the landmark aligned

parameterizations. For genus-0 closed brain surfaces, the optimized spherical

harmonic parameterization, which aligns landmarks to consistent locations on the

sphere, has been widely used. This approach is limited by the loss of bijectivity under

large deformations and the slow computation. In this work, a fast algorithm (called

FLASH) to compute the optimized spherical harmonic parameterization with

consistent landmark alignment is proposed. This is achieved by formulating the

optimization problem to ${overline{mathbb{C}}}$ and thereby linearizing the

problem. Errors introduced near the pole are corrected using quasi-conformal

theories. Also, by adjusting the Beltrami differential of the mapping, a diffeomorphic

(1-1, onto) spherical parameterization can be effectively obtained. The proposed

algorithm has been tested on 38 human brain surfaces. Experimental results

demonstrate that the computation of the landmark aligned spherical harmonic

parameterization is significantly speeded up using the proposed algorithm.

Page 18: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

A Fast Sweeping Method for Computing the Geodesic Distance Map on

Manifolds Represented by the Grid Based Particle Method

Meng WANG

Abstract:

We improve the discretization of Laplace-Beltrami operator defined on the

interface represented by the Grid Based Particle Method (GBPM). Based on this

discretization, we develop a simple iterative scheme to invert the operator on closed

manifolds. As an interesting application, we propose a fast sweeping method for

solving eikonal equations on surfaces. Our analysis and experiments have shown that

the new discretized Laplace-Beltrami operator is nearly diagonally dominant. When

incorporating with a fast sweeping method to obtain the viscosity solution of eikonal

equation on surfaces, the corresponding iterative matrix has spectral radius less than

one.

TEMPO: Teichmuller Extremal Mapping via Point-cloud Optimization

Ting Wei MENG

Abstract:

When solving registration problem, it is important to find conformal mapping

between surfaces. However, with extra constraints (such as landmark constraints)

enforced, conformal mappings generally do not exist. This motivates us to look for

Teichmuller extremal mapping, which satisfies the required constraints while

minimizing the maximal conformality distortion. In this presentation, I will show a

method to compute Teichmuller extremal mapping from surfaces represented by

point cloud to the unit disk with boundary fixed, which can be used for point cloud

registration. The basic idea is to represent the set of diffeomorphisms using Beltrami

coefficients (BCs), and look for an optimal BC associated to the desired Teichmuller

mapping. For the point cloud case, Beltrami coefficients (BCs) is calculated by using

moving least-squares method, so that we can use the Linear Beltrami Solver(LBS) on

point cloud to reconstruct the associated diffeomorphism from the optimal BC.

Therefore, the Teichmuller extremal mapping on point cloud can be calculated from

Quasi-conformal (QC) iterative algorithm.

Page 19: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

Staircasing effect: an experimental view

Zhifeng WU

Abstract:

The total variation regularization method has greatly influenced the imaging

science since L. Rudin and S. Osher introduced the ROF model in the 1990s. The

advantage of total variation consists in preserving edges. However, total variation

regularization tends to make the obtained image cartoonlike, which is called

staircasing effect and is a major drawback of this regularization method. A lot of

effort has been put into modifying the total variation model in order to reduce the

staircasing effect. Two approaches, namely the infimal convolution approach

proposed by A. Chambolle and P. Lions and total generalized variation approach

proposed by K. Bredies and T. Pock, have drew a lot of attention. In this brief talk, I

am glad to show some images reconstructed by adopting the infimal convolution

approach, and analyze the change of staircasing effect when the total variation is

replaced with infimal convolution. Besides, I will try to give an introductory analysis

of the infimal convolution model itself.

A numerical embedding method for solving PDEs on general

geometries

Ningchen YING

Abstract:

In this talk, we will give a method for solving PDEs on surfaces in mathbb{R}^N.

Different with general method for solving PDEs on whole domain, we add a extra

term to the equations which makes the resulting method approximate as solving

PDEs on surface. We illustrate the numerical convergence result for some general

model problem, and also figure out its application to some complex equations.

Page 20: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

Multiple feature iterative hashing

Lifang ZHANG

Abstract:

With the increase of the amount of data and data dimension, classification and

query of the data has become increasingly important. In order to retrieve video,

images, text better, hash methods have emerged in recent years .There have been

many good hash algorithms which have been widely applied in pattern recognition,

machine learning because of its high speed and its adaptability for high - dimensional

data. This paper proposes a new method about multiple feature hash, called multiple

feature iterative hashing (MFIH).The method considers the compact hash code of the

data on a single feature, also considers the impact of relationships between features

on hash codes. Moreover, we get optimal hash codes with iterative quantization.

Experimentsshow thatour methodachieves better efficiencythanother three

hashmethods of single feature.

Video Background and Foreground Modelling

Rui ZHAO

Abstract:

In video analysis, the image foreground detection and background modelling

have many applications on image processing and computer vision. This problem is

challenging if the background is moving or there are so many frames of images with

high resolution in the video. Our aim is to find an efficient way to model the

background then to extract the foreground from the video. Our model can be divided

into two stages: a) Find the static background by maximizing the histogram. 2)

Modeling the background to be the solution a trust region problem with constrains

related to the signal itself and its variations. Practical examples show that our model

is effective and reliable and much quicker.

Page 21: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

A Dictionary-Based Algorithm for Dimensionality Reduction and Data

Reconstruction

Zhong ZHAO

Abstract:

Nonlinear dimensionality reduction (DR) is a basic problem in manifold learning.

However, many DR algorithms cannot deal with the out-of-sample extension

problem and thus cannot be used in large-scale DR problem. Furthermore, many DR

algorithms only consider how to reduce the dimensionality but seldom involve with

how to reconstruct the original high dimensional data from the low dimensional

embeddings (i.e. data reconstruction problem). In this paper, we propose a

dictionary-based algorithm to deal with the out-of-sample extension problem for

large-scale DR task. In this algorithm, we train a high dimensional dictionary and a

low dimensional dictionary corresponding to the high dimensional data and their low

dimensional embedding respectively. With these two dictionaries, dimensionality

reduction and data reconstruction can be easily conducted by coding the input data

point over one dictionary, and then use the code to predict the output data point

over another dictionary. Compared to the existing DR algorithms, our algorithm has

high efficiency since analytic solution is derived. Besides, our reconstruction

algorithm can be applied to many DR algorithms to make them have the ability to

perform data reconstruction. Experiments on synthetic datasets and real world

datasets show that, for both dimensionality reduction and data reconstruction, our

algorithm is accurate and fast.

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Schedule

October 31 Poster Presentation

8:55 p.m.

--9:40 p.m.

Yizun LIN

Fixed-point algorithm based on proximity operator for image denoising

Hao LIU

An idea to improve the result of ROF model by sharpen kernel

convolution

Yoko OKUDA

Linearized alternating direction method for a convex model of material

identification in hyperspectral image

Chao WANG

Determination of regularization parameter inestimation of the Robin

coefficient in the Laplaceequation

Ka Wah WONG

Lax-Friedrichs fast sweeping method for solving eikonal equations on

surfaces

Boxi XU

A Recursive Algorithm for Multi-frequency Acoustic Inverse Source

Problems

Yu YANG

Patch-based Inpainting Using Adaptive Dictionaryby ADMM

Meipeng ZHI

The Regularization Parameter

Page 23: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

November 1 Oral Presentation

9:00 a.m.

Liyuan CHEN

A Convex Variational Model for Restoring Blurred Images with Rician

Noise.

9:12 a.m.

Long CHEN

A novel cell nuclei segmentation method for 3D C. elegans embryonic

time-lapse images

9:24 a.m.

Ka Chun LAM

Optimized Conformal Parameterization with Controllable Area Distortions

9:36 a.m.

Tsz Chun YAM

Comparison of 3 algorithms for computation of Teichmuller extremal

maps

9:48 a.m.

Hulin KUANG

A new fruit recognition method based on multiple features fusion

10:00 a.m.

Hanfang LI

Detecting Alzheimer Disease Patients' Brain Structures with Quasi-

conformal Method

10:12 a.m.

Si Li

Effective noise–suppressed and artifact-reduced reconstruction of

SPECT data using a preconditioned alternating projection algorithm

10:24 a.m. Tea Break

11:00 a.m.

Zhi LI

Color Image Segmentation by Minimal Surface Smoothing

11:12 a.m.

Hongwu LIN

A brief introduction to fMRI

11:24 a.m.

Wenting LONG

High Resolution Image Deblurring with Displacement Errors by using

envl1/TV Model

11:36 a.m. Biao MIN

Page 24: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image

Fast Video Compression Algorithms and Real-Time encoder

implementations

11:48 A.m. End

November 2 Oral Presentation

\9:00 a.m.

Federica SCIACCHIANO

Image reconstruction under non-Gaussian noise

9:12 a.m.

Tat Kin HO

Quasi-conformal parameterizations for multiply-connected domains

9:24 a.m.

Pui Tung CHOI

FLASH: Fast Landmark Aligned Spherical Harmonic Parameterization for

Genus-0 Closed Brain Surfaces

9:48 a.m.

Meng WANG

A Fast Sweeping Method for Computing the Geodesic Distance Map on

Manifolds Represented by the Grid Based Particle Method

10:00 a.m.

Ting Wei MENG

TEMPO: Teichmuller Extremal Mapping via Point-cloud Optimization

10:12 a.m Tea Break

10:45 a.m

Zhifeng WU

Staircasing effect: an experimental view

10:57 a.m

Ningchen YING

A numerical embedding method for solving PDEs on general geometries

11:09 a.m.

Lifang ZHANG

Multiple feature iterative hashing

11:21 a.m.

Rui ZHAO

Video Background and Foreground Modelling

11:33 a.m.

Zhong ZHAO

A Dictionary-Based Algorithm for Dimensionality Reduction and Data

Reconstruction

11:57 a.m. End

Page 25: Posters - math.hkbu.edu.hk › VIISA › HK-GZ2014.pdf · Image inpainting desires to fill in the data in missing area using the information from the observed region of an image