Forward Image Mapping

1
Forward Image Mapping

• Baoquan Chen, Frank Dachile and Arie Kaufman

2
Image Warping

• Geometric transformation between two images
• Plays an important role in CG visualization
• Forward source ? target
• Backward target ? source

3
Perspective Transformation

• Expensive
• At least one division per pixel due to its
  non-linearity
• Decomposition of perspective warping
• To reduce division cost
• Combination of several 1D filtering operation
  doesnt approximate 2D filtering

4
Proposed Method

• One-pass forward warping
• Divisions are reduced to only one per scanline
• Suitable for antialiasing
• Correction of flaws in Gouraud shading
• Optimization of the memory bandwidth

5
Forward Warping Algorithm
6
Forward Warping Algorithm

• Parallel scanlines in the source remain parallel
  in the target
• Equi-distant sample points along a source
  scanline remain equi-distant in the target
  scanline
• ? PP-scanline

7
PP Scanline

• Pixel access becomes regular
• Only two addition are needed to calculate each
  sample point
• Sample point on the target scanline dont
  coincide with target pixels
• ? nearest neighbor

8
PP Scanline Computation

• (u,v) is the source coordinate
• (x,y) is the target coordinate

9
PP Scanline Computation

• A line in the target image ykxB
• (0,0) (1,k) (0,0) (1,k1) ? mapping to source
  image
• because the slopes of two mapped lines are equal

10
Scanline Processing

• Projection of the endpoint from target to source
• Increments are calculated in both x y
• Each source pixel ought to be read 4 time
  (bilinear interpolation)
• Pixel read template is used
• Buffer is used (4 scanline size)

11
Gouraud Shading Correction

• Gouraud shading converts diagonal line into a
  curve in a perspective projection
• Violated the property of preserving lines
• Linear interpolation along a raster in screen
  generally non-linear
• With the special scan direction, linearity is
  preserved

12
Target Pixel Correction

• Linear interpolate the two samples above and
  below every pixels
• Pixel write template is pre-calculated
• Truncate y coordinate value of samples
• Encoded as a series of integer y steps and
  fractional distances dy from the true scanline

13
Target Pixel Correction
14
Antialiasing

• Sample points on the upper scanlines are sparser
  than on the lower scanlines
• Appropriate resampling filter must be used
• Filter footprint conic shape
• Filter profile gaussian filter

15
Result Summary

• Nearly the same speed as affine warping
• Image quality of this method is better than EWA
• Easy to implement in H/W
• Low-pass filtering in one dimension