Image Processing in SIGGRAPH 06

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Image Processing in SIGGRAPH 06

• Speaker Qianqian Hu
• Date March 31, 2006

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Outlines

• Fast Median and Bilateral Filtering
• Ben Weiss (Shell Slate Software)
• Hybrid Images
• Aude Oliva (Massachusetts Institute of
  Technology, Department of Brain and Cognitive
  Sciences), Antonio Torralba (Massachusetts
  Institute of Technology, Computer Science and
  Artificial Intelligence Laboratory), Philippe G.
  Schyns (University of Glasgow)
• Image Deformation Using Moving Least Squares
• Scott Schaefer (Texas AM University), Travis
  McPhail, Joe Warren (Rice University)
• Appearance-Space Texture Synthesis
• Sylvain Lefebvre, Hugues Hoppe (Microsoft
  Research)

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Image Deformation using Moving Least Squares

• Scott Schaefer Travis McPhail
  Joe Warren
• Texas AM University Rice University Rice
  Univeristy

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Example

• 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  

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Previous Work

• Grid-based techniques
• Bivariate cubic splinesSederberg and Parry,
  1986, Lee et al, 1995
• Shepards interpolantBeier and Neely, 1992
• Transformation-based technique
• Radial Basis FunctionBookstein, 1989
• Triangulation-based techniqueIgarashi et al,
  2005

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Overview of SIG05
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Characters of the Deformation Function

• Given a set of handles p, and corresponding new
  positions q. The deformation function f satisfies
• Interpolation f(pi)qi
• Smoothness smooth deformations
• Identity qp ? f(v) v

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Moving Least Squares

• Given a point v in the image, the best affine
  transformation lv(x) minimizes
• where
• DF f(v) lv(v)

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Affine Transformation

• lv(x)xM T,
• M a linear transformation matrix (rotation and
  scaling)
• T a translation
• Best affine transformation
• where

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Least Squares Problem

• where

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Affine Deformations

• Solution for matrix M
• Solution for deformation function

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Result

• Non-uniform scaling and shear

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Similarity Deformations

• Constraints uniform scaling, i.e,
• Define , where
• Least squares problem
• where

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Similarity Deformations

• Solution for matrix M
• Solution for deformation function
• where

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Result

• uniform scaling

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Rigid Deformations

• Constraint no uniform scaling, i.e.,
• Theoretical base

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Rigid Deformations

• Solution for matrix M
• Solution for deformation function
• where , and Ai is as in similarity
  deformations.

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Example

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Examples for Rigid MLS
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Examples for Rigid MLS
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Deformation with Line Segments

• Least squares problem

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Affine Lines

• Line segments are expressed in
  matrix form
• Least squares problem

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Solution

• The deformation function
• and

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Similarity Lines

• The deformation function

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Rigid Lines

• The deformation function
• where

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Examples for Rigid Lines
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Implementation

• Every pixel is replaced by a grid
• Every resulting pixel is calculated using
  bilinear interpolation

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Contributions

• A simple closed-form solution
• a linear system (2X2) at each point
• No use of linear solver
• Simple, and realtime
• Handles
• points,
• line segments.
• As-rigid-as possible

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Shortcoming

• Lack of topological information

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Future Work

• Adding topological information
• Generalizing to 3D to deform surfaces
• Handles can be any curves

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Fast Median and Bilateral Filtering

• Ben Weiss
• Shell Slate Software Corp.

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Example
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Contributions

• Improving Runtime from O(r) to O(logr)
• Scalable to arbitrary radius
• Realtime
• Fitting for any bit-depth

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Related Work

• A variety of O(r) algorithms
• Huang, T.S., 1981. Two-Dimensional Signal
  Processing II Transforms and Median Filters.
• No good performance for large filtering
  kernels.
• A tree-based O(log2r) algorithm
• Gil, J. and Werman, M., 1993. Computing
  2-D Min, Median, and Max Filters.
• Ill-suited for deep-pipelined,
  vector-capable modern processors.
• A parallel algorithm with time complexity of
  O(log4r)
• Ranka, S., and Sahni, S., 1989. Efficient
  Serial and Parallel Algorithms for Median
  Filtering.
• even worser than linear for rlt55.

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Median Filtering

• A pixel value is replaced by the median of its
  neighbours. Tukey, 1977

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Advantages

• Reducing image noise
• Preserving edges
• Basic algorithm of many image-processing
  techniques
• Rank-order filtering
• Morphological processing
• slowness!!!

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Basic O(r) Algorithm

• Consider a r-radius median filter to an 8-bit
  image.

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Histogram and Mean Value

• Use a 256-element histogram
• Mean value the index v such that

Integral 2r22r1
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Huangs O(r) Algorithm
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Fundamental idea

• If multiple columns are processed at once, the
  aforementioned redundant calculations become
  sequential.

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Distributive Histograms

• For disjoint image regions A and B

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Adapted Huangs Algorithm
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Three Tiers and Beyond
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O(logr) Algorithm
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Higher-Depth Median Filtering

• 16-bit and HDR(High dynamic range) images
• Histogram exponentially with bit-depth

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The Ordinal Transform

• cardinal values consecutive ordinal
  values

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Comparison(1)
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Comparison(2)

• For 8-bit data
• 50 times faster than Photoshop
• For 16-bit data
• 20 times as fast as Photoshop
• MedianDemo

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Bilateral Filtering

• A normalized convolutionTomasi, 1998
• Spatial distance
• Relative difference in intensity

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Linear-Intensity Bilateral

• A box spatial and triangular intensity filter

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Logarithmic-Intensity Bilateral

• Durand, F. and Dorsey, J. 2002. Fast Bilateral
  Filtering for the Display of High Dynamic Range
  Images. SIG02

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Example
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Comparison

• BilateralDemo