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This chapter reviews and discusses various aspects of texture analysis. The concentration is on the various methods of extracting textural features from images. The geometric, random field, fractal, and signal processing models of texture are presented. The major classes of texture processing problems such as segmentation, classification, and shape from texture are discussed. The possible application areas of texture such as automated inspection, document processing, and remote sensing are summarized. A bibliography is provided at the end for further reading.

This chapter reviews and discusses various aspects of texture analysis. The concentration is on the various methods of extracting textural features from images. The geometric, random field, fractal, and signal processing models of texture are presented. The major classes of texture processing problems such as segmentation, classification, and shape from texture are discussed. The possible application areas of texture such as automated inspection, document processing, and remote sensing are summarized. A bibliography is provided at the end for further reading.

This chapter presents an introduction to crystallization of organic fine chemicals and pharmaceutical compounds, written for newcomers to the field. The coverage includes the fundamental concepts of solubility, supersaturation, nucleation, growth, and polymorphism. We will also discuss the control of crystal size distribution, crystal shape and purity, and specifically address cooling crystallization and reaction crystallization processes.

In this paper, we present two steps in the process of automatic annotation in archeological images. These steps are feature extraction and feature selection. We focus our research on archeological images which are very much studied in our days. It presents the most important steps in the process of automatic annotation in an image. Feature extraction techniques are applied to get the feature that will be used in classifying and recognizing the images. Also, the selection of characteristics reduces the number of unattractive characteristics. However, we reviewed various images of feature extraction techniques to analyze the archaeological images. Each feature represents one or more feature descriptors in the archeological images. We focus on the descriptor shape of the archaeological objects extraction in the images using contour method-based shape recognition of the monuments. So, the feature selection stage serves to acquire the most interesting characteristics to improve the accuracy of the classification. In the feature selection section, we present a comparative study between feature selection techniques. Then we give our proposal of application of methods of selection of the characteristics of the archaeological images. Finally, we calculate the performance of two steps already mentioned: the extraction of characteristics and the selection of characteristics.

As jumping is an effective method of moving over rough terrain, there is much interest in building robots that can jump. Deformation of a soft robot's body is an effective method to induce jumping. Our aim was to develop a jumping robot by deformation of a circular shell made of spring steel to result in the highest jump. Higher jumping requires enlargement of the contact area between the robot body and the floor. We developed a jumping mechanism that utilized a dish shape to maximize contact area.

The aim of this study was to investigate how the forces required to stabilize the lumbar spine in the standing posture may be affected by variation in its shape. A two-dimensional model of the lumbar spine in the sagittal plane was developed that included a simplified representation of the lumbar extensor muscles. The shape of the model was varied by changing both the magnitude and distribution of the lumbar curvature. The forces required to produce a resultant load traveling along a path as close to the vertebral body centroids as possible (a follower load) were determined. In general,the forces required to produce a follower load increased as the curvature became larger and more evenly distributed. The results suggest that the requirements of the lumbar muscles to maintain spinal stability in vivo will vary between individuals. This has implications for understanding the role of spinal curvature and muscle atrophy in back pain.

This paper contains selected topics from four lectures given at the Abdus Salam International Centre for Theoretical Physics in May 2009. We introduce the study of the influence of knotting and linking on the spatial characteristics of linear and ring polymer chains with examples of scientific interest. We describe a few basic concepts of the geometry and topology of knots and measures of the spatial shape of open and closed polymer chains. We then present some fundamental mathematical results concerning them. Next we discuss random sampling methods of collections of open and closed chains that are employed to provide estimates of the spatial properties of the chains. Finally, we discuss implementations of the sampling algorithms, survey consequences of theoretical and experimental results, and discuss some interesting problems deserving further research.

We present a novel $C^0$-characterization of symplectic embeddings and diffeomorphisms in terms of Lagrangian embeddings. Our approach is based on the shape invariant, which was discovered by Sikorav and Eliashberg, intersection theory and the displacement energy of Lagrangian submanifolds, and the fact that non-Lagrangian submanifolds can be displaced immediately. This characterization gives rise to a new proof of $C^0$-rigidity of symplectic embeddings and diffeomorphisms. The various manifestations of Lagrangian rigidity that are used in our arguments come from $J$-holomorphic curve methods. An advantage of our techniques is that they can be adapted to a $C^0$-characterization of contact embeddings and diffeomorphisms in terms of coisotropic (or pre-Lagrangian) embeddings, which in turn leads to a proof of $C^0$-rigidity of contact embeddings and diffeomorphisms. We give a detailed treatment of the shape invariants of symplectic and contact manifolds, and demonstrate that shape is often a natural language in symplectic and contact topology. We consider homeomorphisms that preserve shape, and propose a hierarchy of notions of Lagrangian topological submanifold. Moreover, we discuss shape-related necessary and sufficient conditions for symplectic and contact embeddings, and define a symplectic capacity from the shape.

This paper introduces a family of rectangularity measures. The measures depend on two parameters which enable their flexibility, i.e. the possibility to adapt with respect to a concrete application. Several rectangularity measures exist in the literature, and they are designed to evaluate numerically how much the shape considered differs from a perfect rectangle. None of these measures distinguishes rectangles whose edge ratios differ, i.e. they assume that all rectangles (including squares) have the same shape. Such property can be a disadvantage in applications. In this paper, we consider differently elongated rectangles to have different shapes, and propose a family of new rectangularity measures which assigns different values to rectangles whose edge ratios differ. The new rectangularity measures are invariant with respect to translation, rotation and scaling transformations. They range over the interval ]0, 1] and attain the value 1 only for perfect rectangles with a desired edge ratio.

The paper stresses the universal role that Cellular Nonlinear Networks (CNNs) are assuming today. It is shown that the dynamical behavior of 3D CNN-based models allows us to approach new emerging problems, to open new research frontiers as the generation of new geometrical forms and to establish some links between art, neuroscience and dynamical systems.