{
  "id": "1601.06044",
  "version": "v1",
  "published": "2016-01-22T15:38:23.000Z",
  "updated": "2016-01-22T15:38:23.000Z",
  "title": "Geometric-Algebra LMS Adaptive Filter and its Application to Rotation Estimation",
  "authors": [
    "Wilder B. Lopes",
    "Anas Al-Nuaimi",
    "Cassio G. Lopes"
  ],
  "comment": "4 pages of content plus 1 of references; 4 figures. Supplementary material (codes and datasets) available at www.lps.usp.br/wilder",
  "categories": [
    "cs.CV",
    "cs.CG"
  ],
  "abstract": "This paper exploits Geometric (Clifford) Algebra (GA) theory in order to devise and introduce a new adaptive filtering strategy. From a least-squares cost function, the gradient is calculated following results from Geometric Calculus (GC), the extension of GA to handle differential and integral calculus. The novel GA least-mean-squares (GA-LMS) adaptive filter, which inherits properties from standard adaptive filters and from GA, is developed to recursively estimate a rotor (multivector), a hypercomplex quantity able to describe rotations in any dimension. The adaptive filter (AF) performance is assessed via a 3D point-clouds registration problem, which contains a rotation estimation step. Calculating the AF computational complexity suggests that it can contribute to reduce the cost of a full-blown 3D registration algorithm, especially when the number of points to be processed grows. Moreover, the employed GA/GC framework allows for easily applying the resulting filter to estimating rotors in higher dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-22T15:38:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric-algebra lms adaptive filter",
      "application",
      "3d point-clouds registration problem",
      "full-blown 3d registration algorithm",
      "af computational complexity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}