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REVIEW OF HEXAGONAL ARRAYS

REVIEW OF HEXAGONAL ARRAYS. Gaurav Baone 01/29/04. OUTLINE . Why Hexagonal? Hexagonal vs. Square Tessellation Coordinate System for hexagonal arrays Hexagonal Sampling Resolution of Hexagonal array images Disadvantages of hexagonal arrays. Why Hexagonal.

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REVIEW OF HEXAGONAL ARRAYS

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  1. REVIEW OF HEXAGONAL ARRAYS Gaurav Baone 01/29/04

  2. OUTLINE • Why Hexagonal? • Hexagonal vs. Square Tessellation • Coordinate System for hexagonal arrays • Hexagonal Sampling • Resolution of Hexagonal array images • Disadvantages of hexagonal arrays

  3. Why Hexagonal... • 3 ways of tiling with regular shapes: • Square: coordinate system easy to use and implement • Triangular: Complicated structure • Hexagonal: Occurs in nature in cases where circular, deformable and under pressure circumstances exist

  4. Hexagonal vs. Square • Hexagonal models the human visual system more precisely • Hexagonal – equidistant 6 neighbours – this helps in representing circular objects

  5. Contd… • Hexagonal tessellation removes the connectivity ambiguity

  6. Contd… • Hexagonal sampling requires 13.4% fewer samples than rectangular sampling • Hexagonal tessellation offers better shape analysis using morphological operations

  7. y v u x Coordinate System • Need • Satisfies all the properties of a cood. System: • Complete • Unique • Convertible • Efficient P p = u u + v v

  8. Contd… • Pixel neighbours : v (u-1,v+1) (u,v+1) (u-1,v) (u,v) (u+1,v) u (u,v-1) (u+1,v-1)

  9. Hexagonal Sampling • Why go for hexagonal sampling? • Process: • The signal has to be circularly band limited at the same frequency as for an equal resolution square image • This reduces the number of sampling points by a factor of 2/(31/2)

  10. Resolution of Hexagonal grid Images • Improved angular resolution due to more lateral neighbours • No aliasing problems in hexagonal arrays

  11. Drawbacks of Hexagonal Arrays • Human vision is comfortable with perpetually straight features which can be observed better in a square array. In the real world such features dominate • Large amount of work has been already done in the area of square arrays and to convert that into hexagonal array may take time.

  12. Thank You

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