Disconnected Skeleton: Shape at its Absolute Scale

We present a new skeletal representation along with a matching framework to address the deformable shape recognition problem. The disconnectedness arises as a result of excessive regularization that we use to describe a shape at an attainably coarse scale. Our motivation is to rely on the stable properties of the shape instead of inaccurately measured secondary details. The new representation does not suffer from the common instability problems of traditional connected skeletons, and the matching process gives quite successful results on a diverse database of 2D shapes. An important difference of our approach from the conventional use of the skeleton is that we replace the local coordinate frame with a global Euclidean frame supported by additional mechanisms to handle articulations and local boundary deformations. As a result, we can produce descriptions that are sensitive to any combination of changes in scale, position, orientation and articulation, as well as invariant ones.Comment: The work excluding {\S}V and {\S}VI has first appeared in 2005 ICCV: Aslan, C., Tari, S.: An Axis-Based Representation for Recognition. In ICCV(2005) 1339- 1346.; Aslan, C., : Disconnected Skeletons for Shape Recognition. Masters thesis, Department of Computer Engineering, Middle East Technical University, May 200

Viscosity Solution

International audienceViscosity solution is a notion of weak solution for a class of partial differential equations of Hamilton-Jacobi type. The range of applications of the notions of viscosity solution and Hamilton-Jacobi equations is enormous, including common class of partial differential equations such as evolutive problems and problems with boundary conditions, equations arising in optimal control theory, differential games, second-order equations arising in stochastic optimal control and stochastic differential games, geometric equations, etc. In computer vision, it also has various applications. In particular, the distance functions which are the viscosity solutions of the Eikonal equations are widely used. Also, all these notions have played an important role in shape representation, morphology, tractography and in general, in image processing. Finally viscosity solutions provide powerful tools to analyse the Shape from shading problem

The research for shape-based visual recognition of object categories

摘要 视觉目标类识别旨在识别图像中特定的某类目标，基于形状的目标类识别是目前计算机视觉研究的热点之一。真实图像中物体姿态的多样性以及环境的复杂性，给目标的形状提取和识别带来巨大挑战。本文借鉴生物视觉机制的研究成果，对基于形状的目标类识别算法进行研究。主要研究内容如下： 1. 研究与形状认知相关的视觉机制，分析形状知觉整体性的生理基础及其生理模型。以形状知觉整体性为基础，建立基于形状的目标类识别系统框架。框架既重视整体性在自下而上的特征加工中的作用，也重视整体约束在自上而下的识别中的作用。 2. 受生物视觉上的整合野模型启发，本文提出了一个三阶段轮廓检测算法。阶段1利用结构自适应滤波器平滑...Categorical object detection addresses determining the number of instances of a particular object category in an image, and localizing those instances in space and scale. The shape-based visual recognition of object categories is one of hot topics in computer vision. The diversity of poses of targets and complexity of the environment in real images bring huge challenges to shape extraction and obj...学位：工学博士院系专业：信息科学与技术学院自动化系_控制理论与控制工程学号：2322006015337

Screened poisson hyperfields for shape coding

We present a novel perspective on shape characterization using the screened Poisson equation. We discuss that the effect of the screening parameter is a change of measure of the underlying metric space. Screening also indicates a conditioned random walker biased by the choice of measure. A continuum of shape fields is created by varying the screening parameter or, equivalently, the bias of the random walker. In addition to creating a regional encoding of the diffusion with a different bias, we further break down the influence of boundary interactions by considering a number of independent random walks, each emanating from a certain boundary point, whose superposition yields the screened Poisson field. Probing the screened Poisson equation from these two complementary perspectives leads to a high-dimensional hyperfield: a rich characterization of the shape that encodes global, local, interior, and boundary interactions. To extract particular shape information as needed in a compact way from the hyperfield, we apply various decompositions either to unveil parts of a shape or parts of a boundary or to create consistent mappings. The latter technique involves lower-dimensional embeddings, which we call screened Poisson encoding maps (SPEM). The expressive power of the SPEM is demonstrated via illustrative experiments as well as a quantitative shape retrieval experiment over a public benchmark database on which the SPEM method shows a high-ranking performance among the existing state-of-the-art shape retrieval methods

Coding shape inside the shape

The shape of an object lies at the interface between vision and cognition, yet the field of statistical shape analysis is far from developing a general mathematical model to represent shapes that would allow computational descriptions to express some simple tasks that are carried out robustly and e↵ortlessly by humans. In this thesis, novel perspectives on shape characterization are presented where the shape information is encoded inside the shape. The representation is free from the dimensions of the shape, hence the model is readily extendable to any shape embedding dimensions (i.e 2D, 3D, 4D). A very desirable property is that the representation possesses the possibility to fuse shape information with other types of information available inside the shape domain, an example would be reflectance information from an optical camera. Three novel fields are proposed within the scope of the thesis, namely ‘Scalable Fluctuating Distance Fields’, ‘Screened Poisson Hyperfields’, ‘Local Convexity Encoding Fields’, which are smooth fields that are obtained by encoding desired shape information. ‘Scalable Fluctuating Distance Fields’, that encode parts explicitly, is presented as an interactive tool for tumor protrusion segmentation and as an underlying representation for tumor follow-up analysis. Secondly, ‘Screened Poisson Hyper-Fields’, provide a rich characterization of the shape that encodes global, local, interior and boundary interactions. Low-dimensional embeddings of the hyper-fields are employed to address problems of shape partitioning, 2D shape classification and 3D non-rigid shape retrieval. Moreover, the embeddings are used to translate the shape matching problem into an image matching problem, utilizing existing arsenal of image matching tools that could not be utilized in shape matching before. Finally, the ‘Local Convexity Encoding Fields’ is formed by encoding information related to local symmetry and local convexity-concavity properties. The representation performance of the shape fields is presented both qualitatively and quantitatively. The descriptors obtained using the regional encoding perspective outperform existing state-of-the-art shape retrieval methods over public benchmark databases, which is highly motivating for further study of regional-volumetric shape representations