Feature Selection. Ardy Goshtasby Wright State University and Image Fusion Systems Research

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1 Feature Selection Ardy Goshtasby Wright State University and Image Fusion Systems Research

2 Image features Points Lines Regions Templates 2

3 Corners They are 1) locally unique and 2) rotationally invariant features. Corners detected at different resolutions. 3

4 Corner-detection using image gradients Given image I: 1. Compute image gradients in x and y directions: Ix, Iy 2. Compute the inertia matrix at each pixel (x,y): C( x, y) = I I x y I I x x where I x and I y are averages of Ix and Iy, respectively, in small neighborhoods centered at (x,y). 3. Compute eigenvalues of C(x,y) and if the smaller eignvalue is locally maximum, take (x,y) as a corner point. I I x y I I y y 4

5 Examples Stable corners: Corners that persist over a wide range of scales or resolutions. Corners detected at two different scales. 5

6 Corner detection using entropy and uniqueness measures Given an image and a threshold distance d: 1. Find edges in the image. 2. At each edge point compute the image entropy within a circular (spherical) window centered at the edge. 3. Remove edges with the lowest p% entropies. 4. Compute the auto-correlation at the remaining edges and save an edge in a list if the largest auto-correlations there is locally minimum. 5. Sort the list from the smallest to the largest auto-correlations. 6. Remove the edge on top of the list and consider it the next corner. 7. Remove all edges from the list that are within distance d of the edge just removed. 8. If more edges remain in the list go to Step 6. Otherwise stop. 6

7 Example Corners in a volumetric MR brain image. Corners shown in stereo. 7

8 Line detection methods By least-squares Using Hough transform Using image gradients 8

9 Least-squares method Given a set of points {(xi,yi): i=1,,n} find ρ and θ of line ρ = xcosθ+ ysinθ such that E is minimum. = n i= 1 ( ρ x i cosθ y i sinθ ) 2 9

10 Example Canny edges Detected lines 10

11 Hough transform A point (x,y) in the xy-plane represents a unique line y = mx + b in the mb-plane, and a point (m,b) in the mb-plane represents to a unique line in the xy-plane. 11

12 Hough transform Parameter m cannot be accurately determined for nearly vertical lines. So, instead of y=mx+b, the polar form of line ρ = xcosθ+ ysinθ is used. Algorithm: Given an edge image: 1. For each edge (x,y), draw curve ρ = xcosθ + ysinθ in the accumulator array ρθ. As the curve is drawn, increment entries of the array falling on the curve by Locate locally peak entries in the array. Each such entry ρθ in the array detects a line in the xy-plane. 12

13 Line detection using image gradients 1. Determine the gradient magnitude and gradient direction of pixels in image. 2. Group the pixels into regions with gradient directions in [ α,α] [α,3α].., where α is a small angle, such as 5 degrees. 3. Remove regions that are smaller than a threshold value. 4. Fit a line to each remaining region by the weighted least-squares method, with the weights being the gradient magnitude at the pixels. 13

14 Example Lines detected at two different resolutions. 14

15 Regions In some images, regions are the best features to use in image registration. Centers of gravity of regions are not sensitive to zero-mean noise. Centers of gravity of regions can be determined with subpixel positional accuracy. Centers of gravity of regions are affine invariant. Regions can be obtained by various image segmentation methods. 15

16 Example Landsat MSS image Smoothed and thresholded image 16

17 Templates Templates are circular image regions that are locally unique and informative. They can be considered circular windows that are centered at corner points. Circular windows make the feature selection process independent of an image s orientation. 17

18 Example Corners Templates 18

19 Reading list 1. L. Kitchen and A. Rosenfeld, Gray-level corner detection, Pattern Recognition Letters, 1: (1982). 2. T. Hartkens, K. Rohr, and H. S. Stiehl, Evaluation of 3-D operators for the detection of anatomical point landmarks in MR and CR images, Computer Vision and Image Understanding, 18: (2002). 3. J. Illingworth and J. Kittler, A survey of the Hough transform, Computer Vision, Graphics, and Image Processing, 44: (1988). 4. J. B. Burns, A. R. Hanson, and E. M. Riseman, Extracting straight lines, IEEE Trans. Pattern Analysis and Machine Intelligence, 8(4): (1986). 5. A. Goshtasby, G. Stockman, and C. Page, A region-based approach to digital image registration with subpixel accuracy, IEEE Trans. Geoscience and Remote Sensing, 24(3): (1986). 6. A. Goshtasby, Template matching in rotated images, IEEE Trans. Pattern Analysis and Machine Intelligence, 7(3): (1985). 19