1. Subpixel edge localization

2. DetectionLocalization Edge pixelsEdge points Integer coordinatesFloat coordinates Pixel precisionSubpixel precision Subpixel edge localization

3. Edge pixel Edge point

4. Analysis of the function G(z) gradient modulus, along the gradient direction, z is the coordinate along the gradient direction Three values are known G(0) at the center of the edge pixel G(-1) at the centrer of the pixel preceding the edge pixel G(+1) at the center of the pixel subsequent to the edge pixel G(0) > G(-1)By definition of edge pixel G(0) > G(+1) Estimate the maximum of G: Not necessarily at the center of the edge pixel

6. Deriche approach: interpolate G(z) by means of a parabola G(-1) G(0) G(-1) maximum

7. Problems edge points from straight lines are not aligned problem arises from the parabola used to approximate G(z)?

8. A possibile solution Use a gaussian approximation of G(z) Fit a gaussian through G(0), G(-1) e G(+1)

9. Why a gaussian? optical system impulse response: gaussian Canny edge detector convolves image with a gaussian kernel  normally distributed localization error Convolution between two gaussians  gaussian

10. Edge point coordinate: c

11. Parabola vs Gaussian

12. parabola gaussian Comparison