Sharp feature identification in a polygon

This thesis presents an efficient algorithm for recognizing and extracting sharp-features from polygonal shapes. As used here, a sharp-feature is a distinct portion of a polygon that is long and skinny. The algorithm executes in O(n^2) time, where n is the number of vertices in the polygon. Experimental results from a Java implementation of the algorithm are also presented

Turning function and shape recognition

The technique of turning function is a powerful method for measuring similarity between two dimensional shapes. The method works well when the boundary of the shape does not contain noise edges. We propose an algorithm for smoothing noise edges by decomposing the boundary into monotone components and smoothing the noise edges in each component. We also present an implementation of the proposed smoothing algorithm

Center of gravity guided signature of planar shapes

Measuring the similarities between two planar shapes is a complex problem. A notion of calculating the signature of a planar shape has been proposed. This signature is a unique feature of the planar shape that differentiates it from other planar shapes. Moreover, the comparison of signatures of two planar shapes helps in determining the degree of similarity between them. In part, researchers have tried to propose effective algorithms to compute the signature of the planar shapes. O\u27Rourke introduced the concept of signature of simple polygons for measuring similarities between two dimensional shapes. We propose to model a generalized notion of signature by considering the center of gravity of polygons. Standard signature is determined by considering the half plane through the edges of the polygon. In the generalized model, we propose to measure signature by considering half plane through the center of gravity of polygons and parallel boundary edges

Fast Mapping onto Census Blocks

Pandemic measures such as social distancing and contact tracing can be enhanced by rapidly integrating dynamic location data and demographic data. Projecting billions of longitude and latitude locations onto hundreds of thousands of highly irregular demographic census block polygons is computationally challenging in both research and deployment contexts. This paper describes two approaches labeled "simple" and "fast". The simple approach can be implemented in any scripting language (Matlab/Octave, Python, Julia, R) and is easily integrated and customized to a variety of research goals. This simple approach uses a novel combination of hierarchy, sparse bounding boxes, polygon crossing-number, vectorization, and parallel processing to achieve 100,000,000+ projections per second on 100 servers. The simple approach is compact, does not increase data storage requirements, and is applicable to any country or region. The fast approach exploits the thread, vector, and memory optimizations that are possible using a low-level language (C++) and achieves similar performance on a single server. This paper details these approaches with the goal of enabling the broader community to quickly integrate location and demographic data.Comment: 8 pages, 7 figures, 55 references; accepted to IEEE HPEC 202

Thinning-free Polygonal Approximation of Thick Digital Curves Using Cellular Envelope

Since the inception of successful rasterization of curves and objects in the digital space, several algorithms have been proposed for approximating a given digital curve. All these algorithms, however, resort to thinning as preprocessing before approximating a digital curve with changing thickness. Described in this paper is a novel thinning-free algorithm for polygonal approximation of an arbitrarily thick digital curve, using the concept of "cellular envelope", which is newly introduced in this paper. The cellular envelope, defined as the smallest set of cells containing the given curve, and hence bounded by two tightest (inner and outer) isothetic polygons, is constructed using a combinatorial technique. This envelope, in turn, is analyzed to determine a polygonal approximation of the curve as a sequence of cells using certain attributes of digital straightness. Since a real-world curve=curve-shaped object with varying thickness, unexpected disconnectedness, noisy information, etc., is unsuitable for the existing algorithms on polygonal approximation, the curve is encapsulated by the cellular envelope to enable the polygonal approximation. Owing to the implicit Euclidean-free metrics and combinatorial properties prevailing in the cellular plane, implementation of the proposed algorithm involves primitive integer operations only, leading to fast execution of the algorithm. Experimental results that include output polygons for different values of the approximation parameter corresponding to several real-world digital curves, a couple of measures on the quality of approximation, comparative results related with two other well-referred algorithms, and CPU times, have been presented to demonstrate the elegance and efficacy of the proposed algorithm

Detection of presence, position and correct positioning of components on a PCB by image processing

Un recorrido por el funcionamiento del procesamiento de imagen y sus diferentes procesos, entrando en diferentes funcionamiento matemáticos de los mismos. Además, voy un poco más allá entrando en procesos adyacentes no imprescindibles del proceso de procesar una imagen, como puede ser el tratamiento que se hace del color o cuando se realiza un realce de una imagen durante el procesamiento de esta. Por último, se cuenta el funcionamiento de las redes neuronales, tanto como funciona matemática y lógicamente una neurona por si sola y un esquema de la misma. Añadiendo como se realizaría una red neuronal para el procesamiento de imagen en Python.Departamento de Organización de Empresas y Comercialización e Investigación de MercadosGrado en Ingeniería en Electrónica Industrial y Automátic

Mathematical Imaging and Surface Processing

Within the last decade image and geometry processing have become increasingly rigorous with solid foundations in mathematics. Both areas are research fields at the intersection of different mathematical disciplines, ranging from geometry and calculus of variations to PDE analysis and numerical analysis. The workshop brought together scientists from all these areas and a fruitful interplay took place. There was a lively exchange of ideas between geometry and image processing applications areas, characterized in a number of ways in this workshop. For example, optimal transport, first applied in computer vision is now used to define a distance measure between 3d shapes, spectral analysis as a tool in image processing can be applied in surface classification and matching, and so on. We have also seen the use of Riemannian geometry as a powerful tool to improve the analysis of multivalued images. This volume collects the abstracts for all the presentations covering this wide spectrum of tools and application domains

Digital Library Services for Three-Dimensional Models

With the growth in computing, storage and networking infrastructure, it is becoming increasingly feasible for multimedia professionals—such as graphic designers in commercial, manufacturing, scientific and entertainment areas—to work with 3D digital models of the objects with which they deal in their domain. Unfortunately most of these models exist in individual repositories, and are not accessible to geographically distributed professionals who are in need of them. Building an efficient digital library system presents a number of challenges. In particular, the following issues need to be addressed: (1) What is the best way of representing 3D models in a digital library, so that the searches can be done faster? (2) How to compress and deliver the 3D models to reduce the storage and bandwidth requirements? (3) How can we represent the user\u27s view on similarity between two objects? (4) What search types can be used to enhance the usability of the digital library and how can we implement these searches, what are the trade-offs? In this research, we have developed a digital library architecture for 3D models that addresses the above issues as well as other technical issues. We have developed a prototype for our 3D digital library (3DLIB) that supports compressed storage, along with retrieval of 3D models. The prototype also supports search and discovery services that are targeted for 3-D models. The key to 3DLIB is a representation of a 3D model that is based on “surface signatures”. This representation captures the shape information of any free-form surface and encodes it into a set of 2D images. We have developed a shape similarity search technique that uses the signature images to compare 3D models. One advantage of the proposed technique is that it works in the compressed domain, thus it eliminates the need for uncompressing in content-based search. Moreover, we have developed an efficient discovery service consisting of a multi-level hierarchical browsing service that enables users to navigate large sets of 3D models. To implement this targeted browsing (find an object that is similar to a given object in a large collection through browsing) we abstract a large set of 3D models to a small set of representative models (key models). The abstraction is based on shape similarity and uses specially tailored clustering techniques. The browsing service applies clustering recursively to limit the number of key models that a user views at any time. We have evaluated the performance of our digital library services using the Princeton Shape Benchmark (PSB) and it shows significantly better precision and recall, as compared to other approaches