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Lecture 14

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Lecture 14

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Lecture 14

  1. 1. OBJECTS LOCALIZATION AND RECOGNITION CS-467 Digital Image Processing 1
  2. 2. Localization and Recognition • Objects localization and recognition are tasks of computer vision • Localization means that the object’s spatial coordinates should be identified • Recognition means that the object’s membership can be identified • There are also situations when these two tasks cannot be separated from each other 2
  3. 3. Cross-Correlation • Cross-correlation is one of the classical tools for solving localization and recognition problems • Cross-correlation (a sliding dot product) is a measure of similarity of two signals 3 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) m f g t f g t f g k f m g k m τ τ ∞ −∞ ∞ =−∞ = ⊕ = + ∫ ∑  
  4. 4. Cross-Correlation Computation • Analogous to the Convolution Theorem, the Fourier transform of the cross-correlation function is equal to the product of the Fourier transform of one of the signals and the complex conjugated Fourier Transform of another signal 4 ( ) ( ) ( )F f g F f F g= ⋅
  5. 5. Cross-Correlation Computation • Following this important property, the cross- correlation function can be easily calculated using the inverse Fourier transform applied to the product of the Fourier transform of one of the signals and the complex conjugated Fourier Transform of another signal 5 ( )( ) ( )1 1 ( ) ( )f g F F f g F F f F g− − = = ⋅ 
  6. 6. Localization and Recognition using Cross-Correlation • If some signal f is contained in some signal g, then the cross-correlation function takes its maximal value at that coordinate starting from f is contained in g • If some image f(x,y) is contained in some image g(x,y), starting from the coordinates , then, their cross-correlation function has a strong global maximum at 6 f g ( )0 0,x y ( )0 0,x y
  7. 7. Implementation • This property is used for localization and recognition of the object f in the image g • To find f in g (or to show that it is not there), it is necessary to zero-pad f up to sizes of g and to find their cross-correlation function. • If it has a strong global maximum, this means that f is located in g starting from the coordinates of this maximum 7 ( )0 0,x y
  8. 8. Example 8 Target Image of interest Cross-Correlation function. Two white points are its two global maxima whose coordinates coincide with the target coordinates

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