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TAMU CSCE 643 - Distinctive Image Features

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Distinctive Image Features from Scale-Invariant Keypoints David G. Lowe – IJCV 2004OverviewSlide 3Motivation …. Why SIFT anyway?Related Work - Corner DetectorsRelated Work - Feature MatchingRelated Work – Stability to ChangesRelated Work – Other FeaturesSIFT – Scale Space Extrema DetectionThe Difference of Gaussian SpaceSlide 11SIFT – Local Extrema DetectionSlide 13Evaluating Edge Responses by Comparing Principle CurvaturesThe Hessian Matrix and Keypoint RejectionSIFT – Orientation AssignmentSIFT – Keypoint DescriptorSlide 18Experiments – Affine ChangeExperiments - Large DatabasesExperiments – Object RecognitionSlide 22Affine SolutionResultsConclusionsFuture WorkDistinctive Image Featuresfrom Scale-Invariant KeypointsDavid G. Lowe – IJCV 2004Brien FlewellingCPSC 643 Presentation 1OverviewIntroductionMotivation for this workRelated WorkCorners and other Local FeaturesInvariant descriptorsSimilar Detection, Different DescriptorOverviewScalar Invariant Feature TransformScale Space Extrema DetectionKeypoint LocalizationOrientation AssignmentKeypoint DescriptorExperiments and TestsAffine Changes, Large Data Bases, Object RecognitionConclusions and Future WorkMotivation …. Why SIFT anyway?Highly Distinctive Features – Good MatchingDetailed Descriptor – High UniquenessInvariance to :Scale – Zoom/ResamplingIn plane RotationPartial Invariance to :Lighting ChangeOut of plane RotationRelated Work - Corner DetectorsMoravec (1981) – Stereo Matching using CornersHarris and Stevens (1988) – Repeatability ImprovementsHarris Corner Detector (1992) – commonly used in Structure from motion Solutions“Large Gradients at a pre-determined scale”Related Work - Feature MatchingZhang and Torr (1995) – Use of correlation, least squares and geometric constraints to match Harris corners over large image ranges and motions.Schmidt and Mohr (1997) – Use of a rotationally invariant feature descriptor for matching images in large databases with Harris corners.Lowe (1999) – Extension of feature descriptors to achieve scale invariance.Related Work – Stability to ChangesCrowley and Parker (1984) – Scale Space Peaks and matching of Tree Structures.Lindberg (1993-94) – Scale Selection for good feature detection performance.(Baumberg, 2000; Tuytelaars and Van Gool, 2000; Mikolajczyk and Schmid, 2002; Schaffalitzky and Zisserman, 2002; Brown and Lowe, 2002). – Affine Covariant FeaturesRelated Work – Other FeaturesNelson and Selinger (1998) – Image ContoursMatas et al., (2002) – Maximally Stable Extremal RegionsCarneiro and Jepson (2002) – Phase Based Local FeaturesSchiele and Crowley (2000) – Multidimensional Histogram DescriptorsSIFT – Scale Space Extrema DetectionScale Space – A 1-parameter function of the image data Gaussian Scale Space - Convolution with a Gaussian Kernel … No False Structure!L(x, y, σ ) = G(x, y, σ) I(x, y)∗G(x, y, σ ) = (1/2πσ2)*exp(-(x2+y2)/(2σ2))Detection of ExtremaD(x, y, σ ) = (G(x, y, kσ) − G(x, y, σ)) I(x, y)∗ = L(x, y, kσ) − L(x, y, σ ).The Difference of Gaussian SpaceFor constant scaling of σ this approximates the Laplacian of Gaussian Approximating the derivative of the Gaussian function with respect to sigma we can obtainSIFT – Scale Space Extrema DetectionConstruct the DOG scale spaceK – factor of separationS – number of S+3 images in the stack for each octaveResample and repeatFor each location compare to its 26 nearest neighbors in scale space retain only minima and maximaSIFT – Local Extrema DetectionSampling of scale space is a balance between density of samples and the arbitrary feature frequenciesTest the reliability of matches over matching tasks vs. sampling frequenciesThe most stable and useful frequencies can be detected with coarse sampling in scale.SIFT – Local Extrema DetectionOnce a Scale Space Extrema is localized:Calculate an interpolated fit for location, scale and ratio of principle curvaturesCompute a local Taylor Series Expansion of the DOG function. Find the Zero crossing of the derivative of this function:Evaluating Edge Responses by Comparing Principle CurvaturesThe DOG space will have a large response to edges.Poorly defined extrema have strong principle curvature along the edge but a weak principle curvature normal to it.We may examine the relationship between principle curvatures by looking at the eigenvalues of the approximated Hessian matrix.The Hessian Matrix and Keypoint RejectionThe Hessian Matrix is approximated using Neighbor DifferencesThe ratio of the square of the trace to the determinant has a special relationship to the eigenvalue ratioSIFT – Orientation AssignmentTo achieve rotational invariance, the local gradient orientations are examined to define a principle direction.A magnitude weighted orientation histogram is calculated using the DOG image of nearest scale.SIFT – Keypoint DescriptorThe keypoint descriptor structures the local image information in the DOG image of nearest scale with respect to the assigned orientation.Inspired by work by Edelman, Intrator, and Poggio (1997), the feature descriptor lists the gradient orientations in a structured vectorSIFT – Keypoint DescriptorThe number of elements in the descriptor vector is calculated by the product of the number of histogram bins and the number of orientation directions typically 4x4x8 = 128Experiments – Affine ChangeThe SIFT descriptor was tested against a database of 40,000 keypoints.The percent repeatability of correct matches vs. affine performs better than 50% for up to 50 degree rotations out of planeExperiments - Large DatabasesExperiments – Object RecognitionThe Process:Match Keypoints Evaluate the Euclidian Distance between Candidate Matches. Retain the minimum if the next best match is not within a threshold standoff distance.Experiments – Object RecognitionWhen searching for the best match a prioritized Best Bin First search is used.For purposes of object recognition a Hough Transform is used to cluster objects in pose spaceLarge Error Bounds, does not account well for affine variations – 4 DOF vs. 6 DOFAffine SolutionWhen a cluster of matches in pose space is identified it is verified geometrically by least


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