An interactive analysis of harmonic and diffusion equations on discrete 3D shapes

AbstractRecent results in geometry processing have shown that shape segmentation, comparison, and analysis can be successfully addressed through the spectral properties of the Laplace–Beltrami operator, which is involved in the harmonic equation, the Laplacian eigenproblem, the heat diffusion equation, and the definition of spectral distances, such as the bi-harmonic, commute time, and diffusion distances. In this paper, we study the discretization and the main properties of the solutions to these equations on 3D surfaces and their applications to shape analysis. Among the main factors that influence their computation, as well as the corresponding distances, we focus our attention on the choice of different Laplacian matrices, initial boundary conditions, and input shapes. These degrees of freedom motivate our choice to address this study through the executable paper, which allows the user to perform a large set of experiments and select his/her own parameters. Finally, we represent these distances in a unified way and provide a simple procedure to generate new distances on 3D shapes

Robust watermarking of point-sampled geometry

We present a new scheme for digital watermarking of point-sampled geometry based on spectral analysis. By extending existing algorithms designed for polygonal data to unstructured point clouds, our method is particularly suited for scanned models, where the watermark can be directly embedded in the raw data obtained from the 3D acquisition device. To handle large data sets efficiently, we apply a fast hierarchical clustering algorithm that partitions the model into a set of patches. Each patch is mapped into the space of eigenfunctions of an approximate Laplacian operator to obtain a decomposition of the patch surface into discrete frequency bands. The watermark is then embedded into the low frequency components to minimize visual artifacts in the model geometry. During extraction, the target model is resampled at optimal resolution using an MLS projection. After extracting a watermark from this model, the corresponding bit stream is analyzed using statistical methods based on correlation. We have applied our method to a number of point-sampled models of different geometric and topological complexity. These experiments show that our watermarking scheme is robust against numerous attacks, including low-pass filtering, resampling, affine transformations, cropping, additive random noise, and combinations of the above

Data Hiding and Its Applications

Data hiding techniques have been widely used to provide copyright protection, data integrity, covert communication, non-repudiation, and authentication, among other applications. In the context of the increased dissemination and distribution of multimedia content over the internet, data hiding methods, such as digital watermarking and steganography, are becoming increasingly relevant in providing multimedia security. The goal of this book is to focus on the improvement of data hiding algorithms and their different applications (both traditional and emerging), bringing together researchers and practitioners from different research fields, including data hiding, signal processing, cryptography, and information theory, among others

Feature Encoding of Spectral Descriptors for 3D Shape Recognition

Feature descriptors have become a ubiquitous tool in shape analysis. Features can be extracted and subsequently used to design discriminative signatures for solving a variety of 3D shape analysis problems. In particular, shape classification and retrieval are intriguing and challenging problems that lie at the crossroads of computer vision, geometry processing, machine learning and medical imaging. In this thesis, we propose spectral graph wavelet approaches for the classification and retrieval of deformable 3D shapes. First, we review the recent shape descriptors based on the spectral decomposition of the Laplace-Beltrami operator, which provides a rich set of eigenbases that are invariant to intrinsic isometries. We then provide a detailed overview of spectral graph wavelets. In an effort to capture both local and global characteristics of a 3D shape, we propose a three-step feature description framework. Local descriptors are first extracted via the spectral graph wavelet transform having the Mexican hat wavelet as a generating kernel. Then, mid-level features are obtained by embedding local descriptors into the visual vocabulary space using the soft-assignment coding step of the bag-of-features model. A global descriptor is subsequently constructed by aggregating mid-level features weighted by a geodesic exponential kernel, resulting in a matrix representation that describes the frequency of appearance of nearby codewords in the vocabulary. In order to analyze the performance of the proposed algorithms on 3D shape classification, support vector machines and deep belief networks are applied to mid-level features. To assess the performance of the proposed approach for nonrigid 3D shape retrieval, we compare the global descriptor of a query to the global descriptors of the rest of shapes in the dataset using a dissimilarity measure and find the closest shape. Experimental results on three standard 3D shape benchmarks demonstrate the effectiveness of the proposed classification and retrieval approaches in comparison with state-of-the-art methods

Spectral methods for multimodal data analysis

Spectral methods have proven themselves as an important and versatile tool in a wide range of problems in the fields of computer graphics, machine learning, pattern recognition, and computer vision, where many important problems boil down to constructing a Laplacian operator and finding a few of its eigenvalues and eigenfunctions. Classical examples include the computation of diffusion distances on manifolds in computer graphics, Laplacian eigenmaps, and spectral clustering in machine learning. In many cases, one has to deal with multiple data spaces simultaneously. For example, clustering multimedia data in machine learning applications involves various modalities or ``views'' (e.g., text and images), and finding correspondence between shapes in computer graphics problems is an operation performed between two or more modalities. In this thesis, we develop a generalization of spectral methods to deal with multiple data spaces and apply them to problems from the domains of computer graphics, machine learning, and image processing. Our main construction is based on simultaneous diagonalization of Laplacian operators. We present an efficient numerical technique for computing joint approximate eigenvectors of two or more Laplacians in challenging noisy scenarios, which also appears to be the first general non-smooth manifold optimization method. Finally, we use the relation between joint approximate diagonalizability and approximate commutativity of operators to define a structural similarity measure for images. We use this measure to perform structure-preserving color manipulations of a given image

Digital watermarking and novel security devices

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

A robust region-adaptive digital image watermarking system

Digital image watermarking techniques have drawn the attention of researchers and practitioners as a means of protecting copyright in digital images. The technique involves a subset of information-hiding technologies, which work by embedding information into a host image without perceptually altering the appearance of the host image. Despite progress in digital image watermarking technology, the main objectives of the majority of research in this area remain improvements in the imperceptibility and robustness of the watermark to attacks. Watermark attacks are often deliberately applied to a watermarked image in order to remove or destroy any watermark signals in the host data. The purpose of the attack is. aimed at disabling the copyright protection system offered by watermarking technology. Our research in the area of watermark attacks found a number of different types, which can be classified into a number of categories including removal attacks, geometry attacks, cryptographic attacks and protocol attacks. Our research also found that both pixel domain and transform domain watermarking techniques share similar levels of sensitivity to these attacks. The experiment conducted to analyse the effects of different attacks on watermarked data provided us with the conclusion that each attack affects the high and low frequency part of the watermarked image spectrum differently. Furthermore, the findings also showed that the effects of an attack can be alleviated by using a watermark image with a similar frequency spectrum to that of the host image. The results of this experiment led us to a hypothesis that would be proven by applying a watermark embedding technique which takes into account all of the above phenomena. We call this technique 'region-adaptive watermarking'. Region-adaptive watermarking is a novel embedding technique where the watermark data is embedded in different regions of the host image. The embedding algorithms use discrete wavelet transforms and a combination of discrete wavelet transforms and singular value decomposition, respectively. This technique is derived from the earlier hypothesis that the robustness of a watermarking process can be improved by using watermark data in the frequency spectrum that are not too dissimilar to that of the host data. To facilitate this, the technique utilises dual watermarking technologies and embeds parts of the watermark images into selected regions of the host image. Our experiment shows that our technique improves the robustness of the watermark data to image processing and geometric attacks, thus validating the earlier hypothesis. In addition to improving the robustness of the watermark to attacks, we can also show a novel use for the region-adaptive watermarking technique as a means of detecting whether certain types of attack have occurred. This is a unique feature of our watermarking algorithm, which separates it from other state-of-the-art techniques. The watermark detection process uses coefficients derived from the region-adaptive watermarking algorithm in a linear classifier. The experiment conducted to validate this feature shows that, on average, 94.5% of all watermark attacks can be correctly detected and identified

Modeling and Simulation in Engineering

The general aim of this book is to present selected chapters of the following types: chapters with more focus on modeling with some necessary simulation details and chapters with less focus on modeling but with more simulation details. This book contains eleven chapters divided into two sections: Modeling in Continuum Mechanics and Modeling in Electronics and Engineering. We hope our book entitled "Modeling and Simulation in Engineering - Selected Problems" will serve as a useful reference to students, scientists, and engineers