Atributos geométricos invariantes às transformações afins para representação de nuvens de pontos e um arcabouço para extração de momentos algébricos

Abstract

Three-dimensional images (3D images) allow a more precise study of shapes and surfaces by means of depth information. Compared to two-dimensional images (2D images), 3D images overcome some limitations impose in some pratical scenarios. However, many application areas still depend on very invasive pre-processing steps in 3D images, often requiring a priori parameterization. Such dependencies of 3D images reflect on the feature extraction step, either limiting the options of methods that can be used or by impairing the extracted attributes and, consequently, the obtained results. The contribution of this work is two-fold: a new representation for 3D images calculated from a point cloud and a feature extraction system framework based on Moments that has the aforementioned format as the only input. Assembled from local surface information and without the need for any parameterized techniques, the format was called RABG Matrix and proposes to solve the problem of the three invariances arising from the transformations of translation, uniform scaling and rotation. The feature extraction framework inherits the invariance properties and is defined in modular terms, allowing the construction of any Moment Invariants. The invariant aspect is evaluated through demonstrations and empirical experiments. The description capacity of the feature extraction framework is tested by designing three Moment Functions which were used in a scenario of classification of individuals from faces represented by point clouds.