Midterm Wed. Local features: detection and description. Today. Last time. Local features: main components. Goal: interest operator repeatability
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1 Midterm Wed. Local features: detection and description Monday March 7 Prof. UT Austin Covers material up until 3/1 Solutions to practice eam handed out today Bring a sheet of notes if you want Review the outlines and notes on course website, accompanying reading in tetbook Last time Image warping based on homography Detecting corner like points in an image Today Local invariant features Detection of interest points (Harris corner detection) Scale invariant blob detection: LoG Description of local patches SIFT : Histograms of oriented gradients Local features: main components 1) Detection: Identify the interest points Goal: interest operator repeatability We want to detect (at least some of) the same points in both images. ) Description:Etract vector feature descriptor surrounding each interest point. (1) [,, (1) 1 1 d ] 3) Matching: Determine correspondence between descriptors in two views () [,, () 1 d ] No chance to find true matches! Yet we have to be able to run the detection procedure independently per image. 1
2 Goal: descriptor distinctiveness We want to be able to reliably determine which point goes with which.? Must provide some invariance to geometric and photometric differences between the two views. Local features: main components 1) Detection: Identify the interest points ) Description:Etract vector feature descriptor surrounding each interest point. 3) Matching: Determine correspondence between descriptors in two views Recall: Corners as distinctive interest points Recall: Corners as distinctive interest points I M w(, y) I y I I y I yi y matri of image derivatives (averaged in neighborhood of a point). Since M is symmetric, we have 1 M X 0 M i i i 0 X T Notation: I I y y I I y y The eigenvalues of M reveal the amount of intensity change in the two principal orthogonal gradient directions in the window. Recall: Corners as distinctive interest points Harris corner detector edge : 1 >> >> 1 corner : 1 and are large, 1 ~ ; flat region 1 and are small; 1) Compute M matri for image window surrounding each piel to get its cornerness score. ) Find points with large corner response (f > threshold) 3) Take the points of local maima, i.e., perform nonmaimum suppression One way to score the cornerness:
3 Harris Detector: Steps Harris Detector: Steps Compute corner response f Harris Detector: Steps Find points with large corner response: f > threshold Harris Detector: Steps Take only the points of local maima of f Harris Detector: Steps Properties of the Harris corner detector Rotation invariant? Yes 1 M X 0 0 X T Scale invariant? 3
4 Properties of the Harris corner detector Rotation invariant? Yes Scale invariant interest points How can we independently select interest points in each image, such that the detections are repeatable across different scales? Scale invariant? No All points will be classified as edges Corner! Automatic scale selection Intuition: Find scale that gives local maima of some function f in both position and scale. What can be the signature function? f Image 1 f Image s 1 region size s region size Recall: Edge detection Recall: Edge detection f Edge f Edge d g d Derivative of Gaussian d g d Second derivative of Gaussian (Laplacian) d f d g Edge = maimum of derivative d g d f Edge = zero crossing of second derivative Source: S. Seitz Source: S. Seitz 4
5 From edges to blobs Edge = ripple Blob = superposition of two ripples Blob detection in D Laplacian of Gaussian: Circularly symmetric operator for blob detection in D maimum Spatial selection: the magnitude of the Laplacian response will achieve a maimum at the center of the blob, provided the scale of the Laplacian is matched to the scale of the blob Slide credit: Lana Lazebnik g g g y Blob detection in D: scale selection g g Laplacian-of-Gaussian = blob detector g y Blob detection in D We define the characteristic scale as the scale that produces peak of Laplacian response filter scales characteristic scale Bastian Leibe img1 img img3 Slide credit: Lana Lazebnik Eample Original image at ¾ the size Original image at ¾ the size 5
6 Scale invariant interest points Interest points are local maima in both position and scale. scale L ( ) Lyy ( ) List of (, y, σ) Squared filter response maps 6
7 Scale-space blob detector: Eample Technical detail We can approimate the Laplacian with a difference of Gaussians; more efficient to implement. L G y Gyy y (,, ) (,, ) (Laplacian) DoG Gyk (,, ) Gy (,, ) (Difference of Gaussians) Image credit: Lana Lazebnik Local features: main components Geometric transformations 1) Detection: Identify the interest points ) Description:Etract vector feature descriptor surrounding each interest point. (1) [,, (1) 1 1 d ] 3) Matching: Determine correspondence between descriptors in two views () [,, () 1 d ] e.g. scale, translation, rotation Photometric transformations Raw patches as local descriptors The simplest way to describe the neighborhood around an interest point is to write down the list of intensities to form a feature vector. But this is very sensitive to even small shifts, rotations. Figure from T. Tuytelaars ECCV 006 tutorial 7
8 SIFT descriptor [Lowe 004] Making descriptor rotation invariant Use histograms to bin piels within sub-patches according to their orientation. 0 Why subpatches? Why does SIFT have some illumination invariance? CSE 576: Computer Vision Rotate patch according to its dominant gradient orientation This puts the patches into a canonical orientation. Image from Matthew Brown SIFT descriptor [Lowe 004] Eample Etraordinarily robust matching technique Can handle changes in viewpoint Up to about 60 degree out of plane rotation Can handle significant changes in illumination Sometimes even day vs. night (below) Fast and efficient can run in real time Lots of code available NASA Mars Rover images Steve Seitz Eample SIFT properties Invariant to Scale Rotation Partially invariant to Illumination changes Camera viewpoint Occlusion, clutter NASA Mars Rover images with SIFT feature matches Figure by Noah Snavely 8
9 Local features: main components Matching local features 1) Detection: Identify the interest points ) Description:Etract vector feature descriptor surrounding each interest point. 3) Matching: Determine correspondence between descriptors in two views Matching local features Ambiguous matches????? Image 1 Image To generate candidate matches, find patches that have the most similar appearance (e.g., lowest SSD) Simplest approach: compare them all, take the closest (or closest k, or within a thresholded distance) Image 1 Image At what SSD value do we have a good match? To add robustness to matching, can consider ratio : distance to best match / distance to second best match If low, first match looks good. If high, could be ambiguous match. Matching SIFT Descriptors Nearest neighbor (Euclidean distance) Threshold ratio of nearest to nd nearest descriptor Lowe IJCV 004 9
10 Etract features Etract features Compute putative matches Etract features Compute putative matches Loop: Hypothesize transformation T (small group of putative matches that are related by T) Etract features Compute putative matches Loop: Hypothesize transformation T (small group of putative matches that are related by T) Verify transformation (search for other matches consistent with T) Etract features Compute putative matches Loop: Hypothesize transformation T (small group of putative matches that are related by T) Verify transformation (search for other matches consistent with T) Applications of local invariant features Wide baseline stereo Motion tracking Panoramas Mobile robot navigation 3D reconstruction Recognition 10
11 Automatic mosaicing Wide baseline stereo [Image from T. Tuytelaars ECCV 006 tutorial] Recognition of specific objects, scenes Schmid and Mohr 1997 Sivic and Zisserman, 003 Summary Interest point detection Harris corner detector Laplacian of Gaussian, automatic scale selection Invariant descriptors Rotation according to dominant gradient direction Histograms for robustness to small shifts and translations (SIFT descriptor) Rothganger et al. 003 Lowe 00 11
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