Introduction Introduction Distinctive Image Features from Distinctive Image Features from Scale Scale- -Invariant Invariant Keypoints Keypoints � Invariance Invariance � � Intensity Intensity � � Scale Scale David G. Lowe � David G. Lowe � Rotation Rotation � presented by, presented by, � Affine Affine � Sudheendra Sudheendra � View point View point � Introduction Related Research Introduction Related Research � SIFT (Scale Invariant Feature Transformation) approach SIFT (Scale Invariant Feature Transformation) approach � � Local features that are invariant to Local features that are invariant to � � translation, rotation, scale, and other imaging parameters translation, rotation, scale, and other imaging parameters � Local interest points Local interest points � � � Features are highly distinctive, each feature finds its correct Features are highly distinctive, each feature finds its correct � � Rover visual obstacle avoidance, Rover visual obstacle avoidance, Moravec Moravec 1981 1981 – – corner corner � match in the database with high probability match in the database with high probability detectors detectors � � Robust against occlusion and clutter Robust against occlusion and clutter � A combined corner and edge detector, Harris and Stephens 1988 A combined corner and edge detector, Harris and Stephens 1988 � – – Harris corner detector Harris corner detector � Rotationally invariant points Rotationally invariant points � � Local Local greyvalue greyvalue invariants for image retrieval, invariants for image retrieval, Schmid Schmid and Mohr and Mohr � 1997 1997 � Scale invariance Scale invariance � � Scale space theory, Scale space theory, Lindeberg Lindeberg 1993 1993 – – identifying appropriate identifying appropriate � scale for features scale for features � Invariance to affine transformation Invariance to affine transformation � SIFT method SIFT method SIFT method SIFT method Feature Extraction Feature Extraction 1. 1. Invariance to Object recognition Object recognition 2. 2. scale Keypoint Detection Search over all scales and image � Match key descriptors of test image to the database of Match key descriptors of test image to the database of � locations for stable interest points features features � Euclidean distance – Euclidean distance – ratio of nearest to second nearest neighbor ratio of nearest to second nearest neighbor � Keypoint Localization � � Best Best- -Bin Bin- -First approximate algorithm First approximate algorithm Fit a quadratic func and find extrema for more accuracy . Hough transform Hough transform � � Invariance to Cluster matched features with a consistent interpretation Cluster matched features with a consistent interpretation � � Orientation Assignment rotation � Vote for all object poses consistent with the feature Vote for all object poses consistent with the feature � Assign an orientaion to the keypoint � � Select clusters with more than 3 features Select clusters with more than 3 features using local gradient information Partial invariance to Affine transformation Affine transformation � � Local image Descriptor viewpoint Solve for affine parameters and perform geometric verification of Solve for affine parameters and perform geometric verification o f � � the object’s pose in the test image the object’s pose in the test image Form a historgram of local gradients around the keypoint. 1
Scale space representation Scale space representation Keypoint detection Keypoint detection (Example) (Example) Goal Goal – – detect detect keypoints keypoints that are invariant to scale that are invariant to scale � � If the scale of the data set is not available then the only way to work with it is to represent it in to work with it is to represent it in � � If the scale of the data set is not available then the only way all possible scales all possible scales – – scale space theory scale space theory � � Scale Scale- -space representation space representation – – one parameter family of images where fine one parameter family of images where fine- -scale image is scale image is information is successively suppressed (smoothened) information is successively suppressed (smoothened) Using some Using some constrainsts constrainsts on scale space functions on scale space functions Lindeberg Lindeberg defines the scale space defines the scale space represention represention � � of an image as of an image as � � And that the maxima and minima of the And that the maxima and minima of the laplacian laplacian of L produce stable image features of L produce stable image features � � Difference of Difference of gaussian gaussian approximates approximates laplacian laplacian of of gaussian gaussian which is required for true scale which is required for true scale invariance invariance Extrema of the difference of of the difference of gaussian gaussian gives interest points gives interest points � � Extrema Different levels in the scale- -space representation of a two space representation of a two- -dimensional image at scale dimensional image at scale � � Different levels in the scale levels levels t t = 0, 2, 8, 32, 128 and 512 together with grey = 0, 2, 8, 32, 128 and 512 together with grey- -level blobs indicating local level blobs indicating local minima at each scale minima at each scale Keypoint Detection (Diagram) Detection (Diagram) Keypoint Keypoint detection detection Keypoint Incrementally convolve with Incrementally convolve with gaussians gaussians seperated seperated by a constant by a constant � � factor k factor k Octave – Octave – doubling of sigma doubling of sigma � � � � Choose k such there are s images in a particular octave (k= 2 Choose k such there are s images in a particular octave (k= 2 1/s 1/s ) ) � Compute Compute DoG DoG from adjacent scales for entire octave from adjacent scales for entire octave � Choose every second row and column from the image convolved Choose every second row and column from the image convolved � � with gaussian with gaussian with twice the width and repeat above steps for the with twice the width and repeat above steps for the next octave next octave Extrema detection detection - - select points in each octave that are greater select points in each octave that are greater � � Extrema than or less than all their neighbors (8 in image space, 9+ 9 with h than or less than all their neighbors (8 in image space, 9+ 9 wit different scales) different scales) Keypoint detection detection Keypoint Localization Localization Keypoint Keypoint Issues Issues � � Frequency of sampling in scale Frequency of sampling in scale 1. 1. � Local Local extrema extrema of of DoG DoG gives approximate location of gives approximate location of � Choosing s (defined previously) Choosing s (defined previously) keypoints – – keypoints Affects the accuracy of the extrema Affects the accuracy of the extrema – – � Accuracy Accuracy – – pixel, scaling factor level pixel, scaling factor level � st and 2 nd derivatives Quadratic function is fit using the 1 st and 2 nd � Quadratic function is fit using the 1 derivatives � at the obtained at the obtained keypoints keypoints � Extrema Extrema of quadratic gives more accurate and stable of quadratic gives more accurate and stable � keypoint location in scale space (x, y, s) keypoint location in scale space (x, y, s) � Accuracy Accuracy - - sub sub- -pixel and sub pixel and sub- -scale level scale level � ∂ ∂ T 2 D 1 D = + + Highest repeatability for 3 scales per octave Highest repeatability for 3 scales per octave T – D ( x ) D x x x – ∂ ∂ 2 x 2 x Frequency of sampling in the spatial domain Frequency of sampling in the spatial domain 2. 2. − 1 Choosing the initial width of the gaussian Choosing the initial width of the gaussian ∂ ∂ – – 2 D D = − x Similar graph for repeatability against initialwidth Similar graph for repeatability against initialwidth provides an provides an ∂ ∂ – – 2 x x optimal value of 1.6 optimal value of 1.6 2
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