Titlebook: Geometric Algebra Computing; in Engineering and C Eduardo Bayro-Corrochano,Gerik Scheuermann Book 2010 Springer-Verlag London Limited 2010

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Engineering Graphics in Geometric Algebraing applications. A?number of example applications are reviewed. Geometric algebra unites many underpinning mathematical concepts in computer graphics such as vector algebra and vector fields, quaternions, kinematics and projective geometry, and it easily deals with geometric objects, operations, an

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Parameterization of 3D Conformal Transformations in Conformal Geometric Algebraations. By providing a 5D algebraic representation of 3D geometric configurations, conformal geometric algebra proves to be very helpful in pose estimation, motion design, and neuron-based machine learning (Bayro-Corrochano et al., J.?Math. Imaging Vis. 24(1):55–81, .; Dorst et al., Geometric Algebr

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Analyzing Real Vector Fields with Clifford Convolution and Clifford–Fourier Transformds. While image processing of scalar data is a well-established discipline, there is a lack of similar methods for vector data. This paper surveys a particular approach defining convolution operators on vector fields using geometric algebra. This includes a corresponding Clifford–Fourier transform i

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Clifford–Fourier Transform for Color Image Processingefine such a transformation using quaternions or Clifford algebras. We focus here on a geometric approach using group actions. The idea is to generalize the usual definition based on the characters of abelian groups by considering group morphisms from ?. to spinor groups Spin(3) and Spin(4). The tra

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Hilbert Transforms in Clifford Analysised to extract global and instantaneous characteristics, such as frequency, amplitude, and phase, from real signals. The multidimensional approach to the Hilbert transform usually is a tensorial one, considering the so-called Riesz transforms in each of the cartesian variables separately. In this pap

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Geometric Neural Computing for 2D Contour and 3D Surface Reconstructiontworks. Our approach is based on the self-organized neural network called Growing Neural Gas (GNG), incorporating versors of the geometric algebra in its neural units; such versors are the transformations that will be determined during the training stage and then applied to a point to approximate th