Bio-inspired Aging Model-Particle Swarm Optimization and Geometric Algebra for Structure from Motion

Arana‐Daniel, Nancy; Villaseñor, Carlos; López-Franco, Carlos; Alanís, Alma Y.

doi:10.1007/978-3-319-12568-8_92

Cited by 2 publications

(3 citation statements)

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“…In this algebra, it is possible to represent points, pairs of points, lines, planes, circles and spheres. Many algorithms for robotics and machine vision [19], e.g., finding path planning algorithms [14], pose estimation [15], structure extraction from motion [16], geometric entity detection [6,7], and robotic mapping algorithms [8,9], have been developed with this algebra.…”

Section: Hyperconformal Geometric Algebramentioning

confidence: 99%

“…In contrast, geometric entities represented by multivectors are suitable for such transformations, because the same operators can be used in every entity. These features make GA suitable to pose estimation [15], movement estimation [16], navigation over rough terrain [14], computation of inverse kinematics [22], object manipulation [23], 3D reconstruction of buildings [6], and other applications in computer graphics [24]. In conclusion, the mapping algorithms based on GA offer a suitable framework for algorithms development.…”

Section: The Best Mathematical Frameworkmentioning

confidence: 99%

“…In the following sections, we show that the multiellipsoidal mapping algorithm is capable of creating information-rich maps with low memory cost and that the entities obtained with the algorithm are even capable of deforming into other quadratic surfaces due to their representation in GA as multivectors. The entities are described in GA; then, the map is suitable for developing new algorithms that work in this algebra, such as path planning [14], pose estimation [15,16], and other tasks [17].…”

Section: Introductionmentioning

confidence: 99%

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Multiellipsoidal Mapping Algorithm

et al. 2018

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The robotic mapping problem, which consists in providing a spatial model of the environment to a robot, is a research topic with a wide range of applications. One important challenge of this problem is to obtain a map that is information-rich (i.e., a map that preserves main structures of the environment and object shapes) yet still has a low memory cost. Point clouds offer a highly descriptive and information-rich environmental representation; accordingly, many algorithms have been developed to approximate point clouds and lower the memory cost. In recent years, approaches using basic and “simple” (i.e., using only planes or spheres) geometric entities for approximating point clouds have been shown to provide accurate representations at low memory cost. However, a better approximation can be implemented if more complex geometric entities are used. In the present paper, a new object-mapping algorithm is introduced for approximating point clouds with multiple ellipsoids and other quadratic surfaces. We show that this algorithm creates maps that are rich in information yet low in memory cost and have features suitable for other robotics problems such as navigation and pose estimation.

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