IMPROVED FOURIER DESCRIPTORS FOR 2 D SHAPE REPRESENTATION

IMPROVED FOURIER DESCRIPTORS FOR 2 -D SHAPE REPRESENTATION Jonas De Vylder, Wilfried Philips Ghent University, Dept. Of Telecommunications and Information Processing http: //telin. ugent. be/ipi Jonas. De. Vylder@telin. UGent. be Why describe shapes? Prior knowledge Shape analysis Similarity Automatic detection of an object in an image is a difficult task. If the expected object has a certain shape, this shape information can be incorporated as a constraint in the detection algorithm. Techniques able to use this information are: ØSnakes ØHough-transform ØActive Shape Models ØRetrieve similar shapes out of a ØClassification of shapes database ØInterpolate between two similar shapes ØTracking of morphological ØUse the descriptors in a metric to changes measure difference Ø… How describe shapes? Fourier Descriptors Invariance Improved FD’s The FD’s can be made invariant to: S(tn+1) Approximate s(t) S(tn) S(t) is not a unique parametisation! Ø translation Ø Scaling Ø Rotation Ø Changing the starting point of S(t) y y An example of a contour An example of a transformed contour S(tn-1) S(0) S(t) is a parameterisation of the contour Ø Bn are chosen to minimize the mean squared distance between S and SN 0 S(0) x 0 Improve the FDapproximation by changing the scanning speed θ(t) of the contour S’(tn+1) S’(tn-1) S’(t) is a different parameterisation of the contour x Ø Gn minimizes: ØSN can easily be calculated using the FFT Ø S*N can be calculated without interpolating S ØBn are called Fourier Descriptors (FD’s) ØGn are called Improved Fourier Descriptors (IFD’s) Results Examples Measurements Ø 436 leaf contours where approximated ØThe database contains 6 different families of leaves ØAll leaves where approximated using 10, 20, …, 50 (Improved) Fourier Descriptors ØTwo different error metrics are used to compare the FD’s and IFD’s: • An average distance between the original and the approximation ØFor both measurements the IFD’s on average approximated over 10% better than the FD’s Original shape 10 FD’s 10 IFD’s Jonas. devylder@telin. ugent. be • A maximum distance between the original and the approximation