Computer Vision: Chamfer System

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Computer VisionChamfer System

• Dr. Edgar Seemann
• seemann_at_pedestrian-detection.com

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• Silhouette Matching

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Chamfer Matching Gavrila Philomin ICCV99
Object shapes
Real-world image of object
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Distance Transform

• Used to compare/align two (typically binary)
  shapes
• Compute for each pixel the distance to the next
  edge pixel
• Here the eculidean distances areapproximated by
  the 2-3 distance

Distance ?
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Distance Transform

• Overlay second shape over distance transform
• Accumulate distances along shape 2
• Find best matching position by an exhaustive
  search
• Distance is not symmetric
• Distance has to be normalized w.r.t. the length
  of the shapes

Distance 14
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Chamfer Matching
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Efficient implementation

• The distance transform can be efficiently
  computed by two scans over the complete image
• Forward-Scan
• Starts in the upper-left corner and moves from
  left to right, top to bottom
• Uses the following mask
• Backward-Scan
• Starts in the lower-right corner and moves from
  right to left, bottom to top
• Uses the following mask

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Forward scan

• We can choose different values for the filter
  mask
• The local distances, d, s and c, in the mask are
  added to the pixel values of the distance map and
  the new value of the zero pixel is the minimum of
  the five sums
• Example

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Advantages and Disadvantages

• Fast
• Distance transform has to be computed only once
• Comparison for each shape location is cheap
• Good performance on uncluttered images (with few
  background structures)
• Bad performance for cluttered images
• Needs a huge number of people silhouettes
• But computation effort increases with the number
  of silhouettes

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Template Hierachy

• To reduce the number of silhouettes to consider,
  silhouettes can be organized in a template
  hierarchy
• For this, the shapes are clustered by similarity

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Search in the hierarchy

• Matching the shapes, then corresponds to a
  traversal of the template hierarchy
• How can we prune search branches to speed up
  matching?
• Thresholds depend on
• Edge detector (likelihood of gaps)
• Silhouette sizes
• Hierarchy level
• Allowed shape variation
• Thresholds are set statisticallyduring training

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Example Detections
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Video
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Coarse-To-Fine Search

• Goal Reduce search effort by discarding unlikely
  regions with minimal computation
• Idea
• Subsample image and searchfirst at a coarse
  scale
• Only consider regions with alow distance when
  searchingfor a match on finer scales
• Again, we have to findreasonable thresholds

Level 1
Level 2
Level 3
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Protector System (Daimler)
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Adding edge orientation

• So far edge orientation has been completely
  ignored
• Idea Consider edge orientation for each pixel

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Edge orientation - The math

• Given two shapes S, C, we can express the chamfer
  distance in the following manner
• The orientation correspondence between two points
  is then measured by
• The combined distance measure

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Statistical Relevance

• Adding statistical relevance of silhouette
  regions further improves the results
  Dimitrijevic06

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Spatio-Temporal templates

• Use multiple successive frames to build a
  spatio-temporal template (TT1,,TN)
• Allow spatial variations of dx, dy (due to motion
  or camera movements)

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Example single-frame vs. 3 frames
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Quantitative Results

• Red spatio-temporal templates statistical
  relevance

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Video

• Restrict detection to a single articulation (when
  legs are in a v-shaped position)
• Spatio-Temporal templates
• Allows more reliable detection of motion
  direction
• Avoids confusions and some false positive
  detections

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Alternatives Earth Movers Distance

• Originally developed to compare histograms
• Idea Find the minimal flow to transform one
  histogram to another
• Example

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Earth movers distance (EMD)
Distance measure basis
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EMD The math

• Variant of the transportation problem (possible
  solutions Stepping Stone Algorithm,
  Transportation-simplex method)
• Constraints
• EMD-Distance

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Advantages and Disadvantages

• Optimizes matching between silhouette and edge
  structure in image
• Enforces one-to-one matchings (unlike chamfer)
• Allows partial matches
• Can deal with arbitrary features
• High computational complexity
• Approximation is possible Graumann, Darrel
  CVPR94