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Summary: Geometric and topological inference deals with the retrieval of information about a geometric object using only a finite set of possibly noisy sample points. It has connections to manifold learning and provides the mathematical and algorithmic foundations of the rapidly evolving field of topological data analysis. Building on a rigorous treatment of simplicial complexes and distance functions, this self-contained book covers key aspects of the field, from data representation and combinatorial questions to manifold reconstruction and persistent homology. It can serve as a textbook for graduate students or researchers in mathematics, computer science and engineering interested in a geometric approach to data science.

The article focuses on in availability of photogrammetric principle of discrete point measurement without the discrete object points and mentions analysis of geometric elements. Topics discussed include line photogrammetry dealing with linear features in image space, use of digital imagery which enables automated extraction of linear features and inserting equations into results in relation between parameters in image and object space.

Due to the huge amount of data carried by images, it is very important to detect and identify the text region as accurately as possible before performing any character recognition. In this paper we describe a text detection algorithm in complex background. It is based on texture and connected components analysis. First we abstract texture regions which usually contain text. Second, we segment the texture regions into suitable objects; the image is segmented into three classes. Finally, we analyze all connected components present in each binary image according to the three classes with the aim to remove non-text regions. Experiments on a benchmark database show the advantages of the new proposed method compared to another one. Especially, our method is insensitive to complex background, font size and color; and offers high precision (83%) and recall(73%) as well. [ABSTRACT FROM AUTHOR]

Chapter 5 of the book "Spherical CR Geometry and Dehn Surgery," by Richard Evan Schwartz is presented. It presents a dictionary that translates between certain spherical CR objects and real hyperbolic objects. Further it mentions that there are perturbations of the hyperbolic structure to account for all but there are finitely many topological types of Dehn fillings.

Chapter 6 of the book "Spherical CR Geometry and Dehn Surgery," by Richard Evan Schwartz is presented. It presents a technical results that feed into the proof of the High School Transcript Studies (HST). It also deal with basic properties of individual horotubes and their functions that defines them.

Chapter one of the e-book "Primary Algebra" is presented. It explores the concepts of understanding patterns and functions for the students of elementary schools. It informs that the patterns are displays of colors, combinations of shapes and geometric designs and repetition of musical sounds. It also informs that functions consider the relationship between the members of one set and members of another set.