A fellow of the Institute of Electrical and Electronic Engineering (IEEE) and the International Association for Pattern Recognition (IAPR), Josef Bigun obtained his Ms and Ph.D. degrees from Linkoping University, Sweden, in 1983 and 1988 respectively. In 1988, he joined the Swiss Federal Institute of Technology in Lausanne where he worked as Adjoint Scientifique until 1998 with the exception that in 1997 he was a visiting professor at the Royal Institute of Technology, (KTH) Stockholm. He has been elected professor to the Signal Analysis Chair, his current position, at Halmstad University and Chalmers Institute of Technology in 1998. He has been in technical and organizational committees of numerous national and international conferences. In particular, he co-chaired the First International Conference on Audio and Video Based Person Authentication in 1997. He has been contributing as a referee or as an editorial board member of international journals including Pattern Recognition Letters and IEEE Image Processing. He has contributed to the initiation and progress of several national and international research projects in computer vision, in particular in biometric person authentication, e.g. the EU projects IT-VIRSBS, ACTS-M2VTS, NOE-BIOSECURE.

• Human and Computer Vision.- Neuronal Pathways of Vision.- Color.- Linear Tools of Vision.- Discrete Images and Hilbert Spaces.- Continuous Functions and Hilbert Spaces.- Finite Extension or Periodic Functions—Fourier Coefficients.- Fourier Transform—Infinite Extension Functions.- Properties of the Fourier Transform.- Reconstruction and Approximation.- Scales and Frequency Channels.- Vision of Single Direction.- Direction in 2D.- Direction in Curvilinear Coordinates.- Direction in ND, Motion as Direction.- World Geometry by Direction in N Dimensions.- Vision in Multiple Directions.- Group Direction and N-Folded Symmetry.- Grouping, Segmentation, and Region Description.- Reducing the Dimension of Features.- Grouping and Unsupervised Region Segregation.- Region and Boundary Descriptors.- Concluding Remarks.

A fellow of the Institute of Electrical and Electronic Engineering (IEEE) and the International Association for Pattern Recognition (IAPR), Josef Bigun obtained his Ms and Ph.D. degrees from Linkoping University, Sweden, in 1983 and 1988 respectively. In 1988, he joined the Swiss Federal Institute of Technology in Lausanne where he worked as Adjoint Scientifique until 1998 with the exception that in 1997 he was a visiting professor at the Royal Institute of Technology, (KTH) Stockholm. He has been elected professor to the Signal Analysis Chair, his current position, at Halmstad University and Chalmers Institute of Technology in 1998. He has been in technical and organizational committees of numerous national and international conferences. In particular, he co-chaired the First International Conference on Audio and Video Based Person Authentication in 1997. He has been contributing as a referee or as an editorial board member of international journals including Pattern Recognition Letters and IEEE Image Processing. He has contributed to the initiation and progress of several national and international research projects in computer vision, in particular in biometric person authentication, e.g. the EU projects IT-VIRSBS, ACTS-M2VTS, NOE-BIOSECURE.

• Human and Computer Vision.- Neuronal Pathways of Vision.- Color.- Linear Tools of Vision.- Discrete Images and Hilbert Spaces.- Continuous Functions and Hilbert Spaces.- Finite Extension or Periodic Functions—Fourier Coefficients.- Fourier Transform—Infinite Extension Functions.- Properties of the Fourier Transform.- Reconstruction and Approximation.- Scales and Frequency Channels.- Vision of Single Direction.- Direction in 2D.- Direction in Curvilinear Coordinates.- Direction in ND, Motion as Direction.- World Geometry by Direction in N Dimensions.- Vision in Multiple Directions.- Group Direction and N-Folded Symmetry.- Grouping, Segmentation, and Region Description.- Reducing the Dimension of Features.- Grouping and Unsupervised Region Segregation.- Region and Boundary Descriptors.- Concluding Remarks.

A fellow of the Institute of Electrical and Electronic Engineering (IEEE) and the International Association for Pattern Recognition (IAPR), Josef Bigun obtained his Ms and Ph.D. degrees from Linkoping University, Sweden, in 1983 and 1988 respectively. In 1988, he joined the Swiss Federal Institute of Technology in Lausanne where he worked as Adjoint Scientifique until 1998 with the exception that in 1997 he was a visiting professor at the Royal Institute of Technology, (KTH) Stockholm. He has been elected professor to the Signal Analysis Chair, his current position, at Halmstad University and Chalmers Institute of Technology in 1998. He has been in technical and organizational committees of numerous national and international conferences. In particular, he co-chaired the First International Conference on Audio and Video Based Person Authentication in 1997. He has been contributing as a referee or as an editorial board member of international journals including Pattern Recognition Letters and IEEE Image Processing. He has contributed to the initiation and progress of several national and international research projects in computer vision, in particular in biometric person authentication, e.g. the EU projects IT-VIRSBS, ACTS-M2VTS, NOE-BIOSECURE.

• Human and Computer Vision.- Neuronal Pathways of Vision.- Color.- Linear Tools of Vision.- Discrete Images and Hilbert Spaces.- Continuous Functions and Hilbert Spaces.- Finite Extension or Periodic Functions—Fourier Coefficients.- Fourier Transform—Infinite Extension Functions.- Properties of the Fourier Transform.- Reconstruction and Approximation.- Scales and Frequency Channels.- Vision of Single Direction.- Direction in 2D.- Direction in Curvilinear Coordinates.- Direction in ND, Motion as Direction.- World Geometry by Direction in N Dimensions.- Vision in Multiple Directions.- Group Direction and N-Folded Symmetry.- Grouping, Segmentation, and Region Description.- Reducing the Dimension of Features.- Grouping and Unsupervised Region Segregation.- Region and Boundary Descriptors.- Concluding Remarks.