ch10a - Ch10 Edge Detection Overview Edge Models Edge...

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Ch10 – Edge Detection • Overview • Edge Models • Edge Detection – Gradient Based – Edge Templates – Laplacian Zero Crossings – Canny Operator • Performance Evaluation • Hough Transform • Conclusion

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Overview • The purpose of edge detection is to locate the boundaries of objects of interest in an image • Edges are normally marked by a discontinuity in brightness, so most edge detection methods are designed to locate these discontinuities • Once edge points are located, they can be linked together to form object boundaries
Edge Models • An edge model describes the intensity transition between an object with brightness A and the background with brightness B – A step edge has a 1 pixel transition from A to A – A ramp edge has an N pixel linear transition

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Edge Models – A roof edge has an U pixel transition from B to A followed by a D pixel transition back to B – A line edge can be modeled as two adjacent step edges or as a roof edge with U=D=1
Edge Models

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Edge Detection • Image derivatives are typically used to locate intensity transitions marking edges in an image – Gradient (1 st derivative) – Templates (1 st derivative) – Laplacian (2 nd derivative) – Canny (2 nd derivative)
Gradient Based • The gradient of an image give us the direction and magnitude of maximum intensity change at every pixel location in an image f ( x , y ) = f / x , f / y ( ) = f x , f y ( ) direction : θ = tan 1 ( f y / f x ) magnitude : f = f x 2 + f y 2 ( ) 1/ 2 f f x + f y

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Gradient Based • To calculate the gradient, we estimate the partial derivatives at each pixel location • This is normally done with small convolution masks dx and dy f x ( x , y ) = f ( x , y ) * dx ( x , y ) f y ( x , y ) = f ( x , y ) * dy ( x , y )
Gradient Based • Some common choices for dx and dy: dx = 1 1 [ ] dy = 1 1 dx = 1 0 0 1 dy = 0 1 1 0 Roberts cross 2 point estimate dx = 1 0 1 [ ] dy = 1 0 1 3 point estimate

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Gradient Based • 3x3 Prewitt masks for dx and dy: dx = 1 0 1 1 0 1 1 0 1 dy = 1 1 1 0 0 0 1 1 1 dx = 0 1 1 1 0 1 1 1 0 dy = 1 1 0 1 0 1 0 1 1
Gradient Based • 3x3 Sobel masks for dx and dy: dx = 0 1 2 1 0 1 2 1 0 dy = 2 1 0 1 0 1 0 1 2 dx = 1 0 1 2 0 2 1 0 1 dy = 1 2 1 0 0 0 1 2 1

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Gradient Based • 3x3 Frei-Chen masks for dx and dy: dx = 0 1 2 1 0 1 1 0 dy = 1 0 1 0 1 0 1 2 dx = 1 0 1 0 2 1 0 1 dy = 1 1 0 0 0 1 1
Gradient Based original image |dx| using Sobel |dy| using |dx|+|dy|

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Gradient Based smoothed image |dx| using Sobel |dy| using |dx|+|dy|
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This note was uploaded on 12/01/2011 for the course CSCE 5013 taught by Professor Staff during the Fall '08 term at Arkansas.

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ch10a - Ch10 Edge Detection Overview Edge Models Edge...

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