Mathematical approaches to digital color image denoising

Many mathematical models have been designed to remove noise from images. Most of them focus on grey value images with additive artificial noise. Only very few specifically target natural color photos taken by a digital camera with real noise. Noise in natural color photos have special characteristics that are substantially different from those that have been added artificially. In this thesis previous denoising models are reviewed. We analyze the strengths and weakness of existing denoising models by showing where they perform well and where they don't. We put special focus on two models: The steering kernel regression model and the non-local model. For Kernel Regression model, an adaptive bilateral filter is introduced as complementary to enhance it. Also a non-local bilateral filter is proposed as an application of the idea of non-local means filter. Then the idea of cross-channel denoising is proposed in this thesis. It is effective in denoising monochromatic images by understanding the characteristics of digital noise in natural color images. A non-traditional color space is also introduced specifically for this purpose. The cross-channel paradigm can be applied to most of the exisiting models to greatly improve their performance for denoising natural color images.Ph.D.Committee Chair: Haomin Zhou; Committee Member: Luca Dieci; Committee Member: Ronghua Pan; Committee Member: Sung Ha Kang; Committee Member: Yang Wan

Variational and Partial Differential Equation Models for Color Image Denoising and Their Numerical Approximations using Finite Element Methods

Image processing has been a traditional engineering field, which has a broad range of applications in science, engineering and industry. Not long ago, statistical and ad hoc methods had been main tools for studying and analyzing image processing problems. In the past decade, a new approach based on variational and partial differential equation (PDE) methods has emerged as a more powerful approach. Compared with old approaches, variational and PDE methods have remarkable advantages in both theory and computation. It allows to directly handle and process visually important geometric features such as gradients, tangents and curvatures, and to model visually meaningful dynamic process such as linear and nonlinear diffusions. Computationally, it can greatly benefit from the existing wealthy numerical methods for PDEs. Mathematically, a (digital) greyscale image is often described by a matrix and each entry of the matrix represents a pixel value of the image and the size of the matrix indicates the resolution of the image. A (digital) color image is a digital image that includes color information for each pixel. For visually acceptable results, it is necessary (and almost sufficient) to provide three color channels for each pixel, which are interpreted as coordinates in some color space. The RGB (Red, Green, Blue) color space is commonly used in computer displays. Mathematically, a RGB color image is described by a stack of three matrices so that each color pixel value of the RGB color image is represented by a three-dimensional vector consisting values from the RGB channels. The brightness and chromaticity (or polar) decomposition of a color image means to write the three-dimensional color vector as the product of its length, which is called the brightness, and its direction, which is defined as the chromaticity. As a result, the chromaticity must lie on the unit sphere S2 in R3. The primary objectives of this thesis are to present and to implement a class of variational and PDE models and methods for color image denoising based on the brightness and chromaticity decomposition. For a given noisy digital image, we propose to use the well-known Total Variation (TV) model to denoise its brightness and to use a generalized p-harmonic map model to denoise its chromaticity. We derive the Euler-Lagrange equations for these models and formulate the gradient descent method (in the name of gradient flows) for computing the solutions of these equations. We then formulate finite element schemes for approximating the gradient flows and implement these schemes on computers using Matlab® and Comsol Multiphysics® software packages. Finally, we propose some generalizations of the p-harmonic map model, and numerically compare these models with the well-known channel-by-channel model

Recent Advances in Steganography

Steganography is the art and science of communicating which hides the existence of the communication. Steganographic technologies are an important part of the future of Internet security and privacy on open systems such as the Internet. This book's focus is on a relatively new field of study in Steganography and it takes a look at this technology by introducing the readers various concepts of Steganography and Steganalysis. The book has a brief history of steganography and it surveys steganalysis methods considering their modeling techniques. Some new steganography techniques for hiding secret data in images are presented. Furthermore, steganography in speeches is reviewed, and a new approach for hiding data in speeches is introduced

Spectral Characterization of a Prototype SFA Camera for Joint Visible and NIR Acquisition

International audienceMultispectral acquisition improves machine vision since it permits capturing more information on object surface properties than color imaging. The concept of spectral filter arrays has been developed recently and allows multispectral single shot acquisition with a compact camera design. Due to filter manufacturing difficulties, there was, up to recently, no system available for a large span of spectrum, i.e., visible and Near Infra-Red acquisition. This article presents the achievement of a prototype of camera that captures seven visible and one near infra-red bands on the same sensor chip. A calibration is proposed to characterize the sensor, and images are captured. Data are provided as supplementary material for further analysis and simulations. This opens a new range of applications in security, robotics, automotive and medical fields

Computational imaging and automated identification for aqueous environments

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2011Sampling the vast volumes of the ocean requires tools capable of observing from a distance while retaining detail necessary for biology and ecology, ideal for optical methods. Algorithms that work with existing SeaBED AUV imagery are developed, including habitat classi fication with bag-of-words models and multi-stage boosting for rock sh detection. Methods for extracting images of sh from videos of longline operations are demonstrated. A prototype digital holographic imaging device is designed and tested for quantitative in situ microscale imaging. Theory to support the device is developed, including particle noise and the effects of motion. A Wigner-domain model provides optimal settings and optical limits for spherical and planar holographic references. Algorithms to extract the information from real-world digital holograms are created. Focus metrics are discussed, including a novel focus detector using local Zernike moments. Two methods for estimating lateral positions of objects in holograms without reconstruction are presented by extending a summation kernel to spherical references and using a local frequency signature from a Riesz transform. A new metric for quickly estimating object depths without reconstruction is proposed and tested. An example application, quantifying oil droplet size distributions in an underwater plume, demonstrates the efficacy of the prototype and algorithms.Funding was provided by NOAA Grant #5710002014, NOAA NMFS Grant #NA17RJ1223, NSF Grant #OCE-0925284, and NOAA Grant #NA10OAR417008

Image Segmentation using PDE, Variational, Morphological and Probabilistic Methods

The research in this dissertation has focused upon image segmentation and its related areas, using the techniques of partial differential equations, variational methods, mathematical morphological methods and probabilistic methods. An integrated segmentation method using both curve evolution and anisotropic diffusion is presented that utilizes both gradient and region information in images. A bottom-up image segmentation method is proposed to minimize the Mumford-Shah functional. Preferential image segmentation methods are presented that are based on the tree of shapes in mathematical morphologies and the Kullback-Leibler distance in information theory. A thorough evaluation of the morphological preferential image segmentation method is provided, and a web interface is described. A probabilistic model is presented that is based on particle filters for image segmentation. These methods may be incorporated as components of an integrated image processed system. The system utilizes Internet Protocol (IP) cameras for data acquisition. It utilizes image databases to provide prior information and store image processing results. Image preprocessing, image segmentation and object recognition are integrated in one stage in the system, using various methods developed in several areas. Interactions between data acquisition, integrated image processing and image databases are handled smoothly. A framework of the integrated system is implemented using Perl, C++, MySQL and CGI. The integrated system works for various applications such as video tracking, medical image processing and facial image processing. Experimental results on this applications are provided in the dissertation. Efficient computations such as multi-scale computing and parallel computing using graphic processors are also presented

영상 잡음 제거와 수중 영상 복원을 위한 정규화 방법

학위논문(박사)--서울대학교 대학원 :자연과학대학 수리과학부,2020. 2. 강명주.In this thesis, we discuss regularization methods for denoising images corrupted by Gaussian or Cauchy noise and image dehazing in underwater. In image denoising, we introduce the second-order extension of structure tensor total variation and propose a hybrid method for additive Gaussian noise. Furthermore, we apply the weighted nuclear norm under nonlocal framework to remove additive Cauchy noise in images. We adopt the nonconvex alternating direction method of multiplier to solve the problem iteratively. Subsequently, based on the color ellipsoid prior which is effective for restoring hazy image in the atmosphere, we suggest novel dehazing method adapted for underwater condition. Because attenuation rate of light varies depending on wavelength of light in water, we apply the color ellipsoid prior only for green and blue channels and combine it with intensity map of red channel to refine the obtained depth map further. Numerical experiments show that our proposed methods show superior results compared with other methods both in quantitative and qualitative aspects.본 논문에서 우리는 가우시안 또는 코시 분포를 따르는 잡음으로 오염된 영상과 물 속에서 얻은 영상을 복원하기 위한 정규화 방법에 대해 논의한다. 영상 잡음 문제에서 우리는 덧셈 가우시안 잡음의 해결을 위해 구조 텐서 총변이의 이차 확장을 도입하고 이것을 이용한 혼합 방법을 제안한다. 나아가 덧셈 코시 잡음 문제를 해결하기 위해 우리는 가중 핵 노름을 비국소적인 틀에서 적용하고 비볼록 교차 승수법을 통해서 반복적으로 문제를 푼다. 이어서 대기 중의 안개 낀 영상을 복원하는데 효과적인 색 타원면 가정에 기초하여, 우리는 물 속의 상황에 알맞은 영상 복원 방법을 제시한다. 물 속에서 빛의 감쇠 정도는 빛의 파장에 따라 달라지기 때문에, 우리는 색 타원면 가정을 영상의 녹색과 청색 채널에 적용하고 그로부터 얻은 깊이 지도를 적색 채널의 강도 지도와 혼합하여 개선된 깊이 지도를 얻는다. 수치적 실험을 통해서 우리가 제시한 방법들을 다른 방법과 비교하고 질적인 측면과 평가 지표에 따른 양적인 측면 모두에서 우수함을 확인한다.1 Introduction 1 1.1 Image denoising for Gaussian and Cauchy noise 2 1.2 Underwater image dehazing 5 2 Preliminaries 9 2.1 Variational models for image denoising 9 2.1.1 Data-fidelity 9 2.1.2 Regularization 11 2.1.3 Optimization algorithm 14 2.2 Methods for image dehazing in the air 15 2.2.1 Dark channel prior 16 2.2.2 Color ellipsoid prior 19 3 Image denoising for Gaussian and Cauchy noise 23 3.1 Second-order structure tensor and hybrid STV 23 3.1.1 Structure tensor total variation 24 3.1.2 Proposed model 28 3.1.3 Discretization of the model 31 3.1.4 Numerical algorithm 35 3.1.5 Experimental results 37 3.2 Weighted nuclear norm minimization for Cauchy noise 46 3.2.1 Variational models for Cauchy noise 46 3.2.2 Low rank minimization by weighted nuclear norm 52 3.2.3 Proposed method 55 3.2.4 ADMM algorithm 56 3.2.5 Numerical method and experimental results 58 4 Image restoration in underwater 71 4.1 Scientific background 72 4.2 Proposed method 73 4.2.1 Color ellipsoid prior on underwater 74 4.2.2 Background light estimation 78 4.3 Experimental results 80 5 Conclusion 87 Appendices 89Docto