Image Interpolation Methods using E-spline

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Image Interpolation Methods using E-spline

• lbg_at_dongseo.ac.kr
• http//kowon.dongseo.ac.kr/lbg/

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B-spline Interpolation Kernel
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B-spline basis functions
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Recursive Formula for B-spline
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Refinement relation for B-spline
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Repeated integration for B-spline
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E-spline
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• E30splineftproc(a, t)local r
• r(-a12exp(a3)a2a1exp(a2)a42a
  1exp(a3)a22a12exp(a2)a3-a12
  exp(a2)a4a12exp(a3)a4exp(a3)a4
  2a2-exp(a3)a22a4-exp(a1)a22a
  3a22exp(a1)a4-a1exp(a3)a42-a1
  exp(a2)a32exp(a1)a42a3exp(a1)
  a2a32-a2exp(a1)a42exp(a4)a1
  2a2-exp(a2)a42a3exp(a2)a4a32
  -exp(a1)a4a32exp(a4)a22a3-exp(a
  4)a1a22-exp(a4)a12a3-exp(a4)a
  2a32exp(a4)a1a32)/(-a1a4a3
  a32a1a1a4a2-a1a3a2-a33
  a4a32-a3a4a2a32a2)/(-a12a
  2a1a4a1-a4a2)/(-a2a4)/(2(-a
  12exp(a3)a2a1exp(a2)a42a1exp
  (a3)a22a12exp(a2)a3-a12exp(a2
  )a4a12exp(a3)a4exp(a3)a42a2
  -exp(a3)a22a4-exp(a1)a22a3a2
  2exp(a1)a4-a1exp(a3)a42-a1exp(a
  2)a32exp(a1)a42a3exp(a1)a2a
  32-a2exp(a1)a42exp(a4)a12a2-
  exp(a2)a42a3exp(a2)a4a32-exp(a
  1)a4a32exp(a4)a22a3-exp(a4)a
  1a22-exp(a4)a12a3-exp(a4)a2a3
  2exp(a4)a1a32)/(-a1a4a3a32
  a1a1a4a2-a1a3a2-a33a4a
  32-a3a4a2a32a2)/(-a12a2a1
  a4a1-a4a2)/(-a2a4)/(2(-a12ex
  p(a3)a2a1exp(a2)a42a1exp(a3)
  a22a12exp(a2)a3-a12exp(a2)a4
  a12exp(a3)a4exp(a3)a42a2-exp(a
  3)a22a4-exp(a1)a22a3a22exp(
  a1)a4-a1exp(a3)a42-a1exp(a2)a
  32exp(a1)a42a3exp(a1)a2a32-a
  2exp(a1)a42exp(a4)a12a2-exp(a2
  )a42a3exp(a2)a4a32-exp(a1)a4
  a32exp(a4)a22a3-exp(a4)a1a2
  2-exp(a4)a12a3-exp(a4)a2a32exp
  (a4)a1a32)/(-a1a4a3a32a1a
  1a4a2-a1a3a2-a33a4a32-a
  3a4a2a32a2)/(-a12a2a1a4
  a1-a4a2)/(-a2a4)-(-exp(a4)exp(a2)
  a32a2-exp(a4)a2exp(a1)a42-exp(a
  4)a22exp(a3)a4exp(a4)a2exp(a3
  )a42a1exp(a3)exp(a2)a22-exp(a2)
  exp(a3)a1a32-a12exp(a2)exp(a1)
  a4exp(a4)exp(a2)a32a4exp(a4)exp
  (a1)a42a3exp(a4)exp(a3)a22a3
  -a2exp(a1)exp(a2)a42-exp(a4)a12
  exp(a3)a3-exp(a4)exp(a2)a42a3-exp
  (a4)exp(a1)a4a32-exp(a4)a12exp(
  a1)a3-exp(a4)exp(a3)a32a2-exp(a2
  )exp(a1)a1a32a1exp(a3)exp(a1)
  a22-exp(a4)a1exp(a2)a22-exp(a4)a
  1exp(a3)a42-exp(a4)a1exp(a1)a2
  2exp(a1)exp(a3)a3a42exp(a3)exp(a
  1)a12a4-a12exp(a3)exp(a2)a2a
  12exp(a2)exp(a1)a3a12exp(a2)ex
  p(a3)a3-a12exp(a3)exp(a1)a2-exp(a
  1)exp(a2)a22a3exp(a4)a22exp(a
  1)a4exp(a4)exp(a1)a1a32exp(a1)
  exp(a3)a32a2exp(a2)exp(a3)a4a
  32-exp(a1)exp(a3)a22a3-exp(a1)exp
  (a3)a4a32a22exp(a1)exp(a2)a4
  -exp(a2)exp(a3)a42a3-exp(a4)exp(a2
  )a12a4exp(a4)exp(a2)a42a1exp
  (a4)exp(a3)a1a32exp(a1)exp(a2)a
  32a2-a22exp(a3)exp(a2)a4exp(a4
  )a12exp(a2)a2a1exp(a2)exp(a1)
  a42exp(a4)a12exp(a1)a2-exp(a3)e
  xp(a1)a42a1a2exp(a3)exp(a2)a4
  2exp(a4)a12exp(a3)a4exp(a4)exp(a
  2)a22a3)/(-a1a4a2-a1a3a2
  a3a4a2a2a12a4a12-a13-a1
  a4a3a3a12)/(a4a2-a4a3a3
  a2-a22)/(-a3a4))-(-exp(a4)exp(a2)a
  32a2-exp(a4)a2exp(a1)a42-exp(a4
  )a22exp(a3)a4exp(a4)a2exp(a3)
  a42a1exp(a3)exp(a2)a22-exp(a2)e
  xp(a3)a1a32-a12exp(a2)exp(a1)a
  4exp(a4)exp(a2)a32a4exp(a4)exp(a
  1)a42a3exp(a4)exp(a3)a22a3-a
  2exp(a1)exp(a2)a42-exp(a4)a12ex
  p(a3)a3-exp(a4)exp(a2)a42a3-exp(a
  4)exp(a1)a4a32-exp(a4)a12exp(a
  1)a3-exp(a4)exp(a3)a32a2-exp(a2)
  exp(a1)a1a32a1exp(a3)exp(a1)a
  22-exp(a4)a1exp(a2)a22-exp(a4)a1
  exp(a3)a42-exp(a4)a1exp(a1)a22
  exp(a1)exp(a3)a3a42exp(a3)exp(a1
  )a12a4-a12exp(a3)exp(a2)a2a1
  2exp(a2)exp(a1)a3a12exp(a2)exp(
  a3)a3-a12exp(a3)exp(a1)a2-exp(a1
  )exp(a2)a22a3exp(a4)a22exp(a1
  )a4exp(a4)exp(a1)a1a32exp(a1)e
  xp(a3)a32a2exp(a2)exp(a3)a4a3
  2-exp(a1)exp(a3)a22a3-exp(a1)exp(a
  3)a4a32a22exp(a1)exp(a2)a4-e
  xp(a2)exp(a3)a42a3-exp(a4)exp(a2)
  a12a4exp(a4)exp(a2)a42a1exp(a
  4)exp(a3)a1a32exp(a1)exp(a2)a3
  2a2-a22exp(a3)exp(a2)a4exp(a4)
  a12exp(a2)a2a1exp(a2)exp(a1)a
  42exp(a4)a12exp(a1)a2-exp(a3)exp
  (a1)a42a1a2exp(a3)exp(a2)a42
  exp(a4)a12exp(a3)a4exp(a4)exp(a2
  )a22a3)/(-a1a4a2-a1a3a2a
  3a4a2a2a12a4a12-a13-a1a
  4a3a3a12)/(a4a2-a4a3a3a
  2-a22)/(-a3a4)/(2(-a12exp(a3)a2
  a1exp(a2)a42a1exp(a3)a22a1
  2exp(a2)a3-a12exp(a2)a4a12exp(
  a3)a4exp(a3)a42a2-exp(a3)a22
  a4-exp(a1)a22a3a22exp(a1)a4-a
  1exp(a3)a42-a1exp(a2)a32exp(a1
  )a42a3exp(a1)a2a32-a2exp(a1
  )a42exp(a4)a12a2-exp(a2)a42a
  3exp(a2)a4a32-exp(a1)a4a32exp
  (a4)a22a3-exp(a4)a1a22-exp(a4)
  a12a3-exp(a4)a2a32exp(a4)a1
  a32)/(-a1a4a3a32a1a1a4a2
  -a1a3a2-a33a4a32-a3a4a2
  a32a2)/(-a12a2a1a4a1-a4a
  2)/(-a2a4)-(-exp(a4)exp(a2)a32a2
  -exp(a4)a2exp(a1)a42-exp(a4)a22
  exp(a3)a4exp(a4)a2exp(a3)a42a1
  exp(a3)exp(a2)a22-exp(a2)exp(a3)a
  1a32-a12exp(a2)exp(a1)a4exp(a4
  )exp(a2)a32a4exp(a4)exp(a1)a4
  2a3exp(a4)exp(a3)a22a3-a2exp(a
  1)exp(a2)a42-exp(a4)a12exp(a3)a
  3-exp(a4)exp(a2)a42a3-exp(a4)exp(a
  1)a4a32-exp(a4)a12exp(a1)a3-e
  xp(a4)exp(a3)a32a2-exp(a2)exp(a1)
  a1a32a1exp(a3)exp(a1)a2

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Truncated powers for B-spline
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Truncated Exponential
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Truncated Exponential (n1)
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Truncated Exponential (n2)
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Truncated Exponential (n3)
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Truncated Exponential (n4)
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E-spline (n)
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Linear E-spline
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Linear E-spline
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Linear E-spline
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Linear E-spline
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Normalized Linear E-spline
Partition of unity
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Quadratic E-spline
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Cubic E-spline
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Quadratic E-spline
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Quadratic E-spline
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Quadratic E-spline
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Cubic E-spline
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Cross-sectional Volumes
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Cross-sectional Volumes for subcubes
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Box-spline as Cross-sectional Volumes
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Bivariate Box spline over triangular grid
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Image Interpolation Methods
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h(x) Kernel functions
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h(x) Kernel functions
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Cubic Interpolation
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B-spline Approximation
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B-spline Interpolation
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Discrete B-spline Interpolation
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Discrete E-spline Interpolation
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Discrete E-spline Interpolation