Ridge and valley are the main components in an image, especially in fingerprints.

1. Ridge and valley are the main components in an image, especially in fingerprints. • What is ridge and valley? • How do we detect them?

2. Ridge and valley

3. Ridge and valley • Intuition: a sequence of pixels having intensity values higher(lower) than those neighboring sequence. • The meeting curve of two ascending (descending) surfaces.

5. Intuitive methods • Intuitive method is to extract the zero-crossings of the first directional derivative taken in a direction which extremizes the second directional derivative. • First directional derivative: • For details see R. Haralick(1983)

6. Height condition • Haralick’s idea can be extended to d dimensional images. • Let be a d-D images. is its gradient and is its Hessian matrix. • Let be the eigenvalues of and be their corresponding eigenvetors.

7. Height condition(cont.) • A n-D( )ridge(valley) can be characterized as: and if ridge if valley See paper “Ridges for Image Analysis” (1994)

8. Other methods • In Jain’s work[1997], ridges are obtained by convolution with two masks. • In O’Gorman and Nickerson’s work[1989], a k by k spatial filter mask is used for labeling the pixels as foreground or background. • Mehtre and Chatterjee[1989] described a method based on some statistics of the local orientations of the ridges of the original image.

9. Combinatorial Classification • I mainly introduce this classification of pixels for ridge extraction in a gray-scale fingerprint image. • Two-fold process: a new combinatorial pixel classification scheme for ridge extraction and a binary thinning of the ridges.

10. Three classes of pixels • Ridge, valley and slope.

11. Directions and gradients • We can compute the directional gradients for every pixel based on their neighbor pixel values. • 4 directions • Sign of the gradients

12. Classification • Based on the 4 directional gradients we classify every pixel by a look-up table. • Preliminary classification • Final classification based on average pixel value on the k-size neighborhood

13. Thinning • The image after the above operation reduces to 2 or 3-pixel thick ridge line and valley line. • Ridges are treated as foreground and valleys and slopes are treated as background. • Standard thinning techniques on this binary image.