1. Object Recognition with Invariant Features n Definition: Identify objects or scenes and determine their pose and model parameters n Applications l Industrial automation and inspection l Mobile robots, toys, user interfaces l Location recognition l Digital camera panoramas l 3D scene modeling, augmented reality by David Lowe

2. Zhang, Deriche, Faugeras, Luong (95) n Apply Harris corner detector n Match points by correlating only at corner points n Derive epipolar alignment using robust least-squares

3. Cordelia Schmid & Roger Mohr (97) n Apply Harris corner detector n Use rotational invariants at corner points l However, not scale invariant. Sensitive to viewpoint and illumination change.

4. Invariant Local Features n Image content is transformed into local feature coordinates that are invariant to translation, rotation, scale, and other imaging parameters SIFT Features

5. Advantages of invariant local features n Locality: features are local, so robust to occlusion and clutter (no prior segmentation) n Distinctiveness: individual features can be matched to a large database of objects n Quantity: many features can be generated for even small objects n Efficiency: close to real-time performance n Extensibility: can easily be extended to wide range of differing feature types, with each adding robustness

6. Build Scale-Space Pyramid n All scales must be examined to identify scale-invariant features n An efficient function is to compute the Difference of Gaussian (DOG) pyramid (Burt & Adelson, 1983)

7. Key point localization n Detect maxima and minima of difference-of-Gaussian in scale space

8. Select canonical orientation n Create histogram of local gradient directions computed at selected scale n Assign canonical orientation at peak of smoothed histogram n Each key specifies stable 2D coordinates (x, y, scale, orientation)

9. Example of keypoint detection Threshold on value at DOG peak and on ratio of principle curvatures (Harris approach) (a) 233x189 image (b) 832 DOG extrema (c) 729 left after peak value threshold (d) 536 left after testing ratio of principle curvatures

10. SIFT vector formation n Thresholded image gradients are sampled over 16x16 array of locations in scale space n Create array of orientation histograms n 8 orientations x 4x4 histogram array = 128 dimensions

11. Feature stability to noise n Match features after random change in image scale & orientation, with differing levels of image noise n Find nearest neighbor in database of 30,000 features

12. Feature stability to affine change n Match features after random change in image scale & orientation, with 2% image noise, and affine distortion n Find nearest neighbor in database of 30,000 features

13. Distinctiveness of features n Vary size of database of features, with 30 degree affine change, 2% image noise n Measure % correct for single nearest neighbor match

14. Detecting 0.1% inliers among 99.9% outliers n We need to recognize clusters of just 3 consistent features among 3000 feature match hypotheses n LMS or RANSAC would be hopeless! n Generalized Hough transform l Vote for each potential match according to model ID and pose l Insert into multiple bins to allow for error in similarity approximation

15. Model verification 1. Examine all clusters with at least 3 features 2. Perform least-squares affine fit to model. 3. Discard outliers and perform top-down check for additional features. 4. Evaluate probability that match is correct  Use Bayesian model, with probability that features would arise by chance if object was not present (Lowe, CVPR 01)

16. Solution for affine parameters n Affine transform of [x,y] to [u,v]: n Rewrite to solve for transform parameters:

17. 3D Object Recognition n Extract outlines with background subtraction n Store keypoint locations and SIFT descriptors in a database

18. 3D Object Recognition n Only 3 keys are needed for recognition, so extra keys provide robustness n Affine model is no longer as accurate

19. Recognition under occlusion

20. Test of illumination invariance n Same image under differing illumination 273 keys verified in final match

21. Location recognition