Object Recognition Using Template Matching

• The old way: from viewer-centered to object-centered representations
  • Edge detection, edge linking
  • Shape from shading, line labeling
  • Volume description matched against description in library of known objects
• The new way: avoid object description; shape is implicit in sets of views of objects
  • For each known object, library contains a model, a set of images, each consisting of identifiable feature points
  • For each unknown, for each model, correspondences are set up between points in the unknown and feature points in the model images
  • Based on the correspondences, predictions are made about where other points in the unknown should appear, resulting in a custom-made template for each model
  • The unknown is identified as an instance of the category associated with the model template which matches best

Points in Rotated Images

• Coordinate system and orthographic projections
• Rotation about y axis: what happens to x
  
• x after 3 different rotations
  
• Correspondences between two points in unknown and in two model images permit solving for and predicting location of other points in unknown
  

Arbitrary Rotation and Translation

• Coordinates after arbitrary rotation and translation
  
• x after 4 different rotations
  
• Correspondences between 4 points in unknown and in 3 model images permit solving for , and predicting location of other points in unknown
  
• Analogous reasoning for y

Object Recognition Algorithm

• Until a satisfactory match is made or there are no more models in the model library,
  • Find four corresponding points in the observed image and in a model's three library images.
  • Use the corresponding points to determine the coefficients, alpha and beta, used to predict the x and y coordinate values of other image points.
  • Determine whether a satisfactory match is made by comparing the predicted x and y coordinate values with those actually found in the observed image.
• If a satisfactory match occurs, announce the identity of the unknown; otherwise, announce failure.

Establishing Point Correspondences

• Tracking points as object is moved slowly
• Otherwise, knowing correspondences among sets of points is enough
• In y rotation case, for two points
  
• Permits solving for coefficients without knowing which point in one set corresponds to which point in another
• For y rotation, need 2 corresponding sets of points in 2 images; for arbitrary rotation and translation, need 4 corresponding sets of points in 3 images
• Heuristics for finding correspondences of sets of points, e.g., looking for natural tops and bottoms

Object Recognition: An Example

• Given x positions after three rotations, find fourth
  
• We can solve for xU,
  
• The model images and the unknown
  
• (x,y) coordinates of 5 points in 3 rotations of known (model) and in unknown
  
• To find coefficients
  
• 
• Where Point 5 should be in the unknown if there is a match: (1.3111, 1.2018)