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Object Recognition using Local Descriptors Javier Ruiz-del-Solar, and Patricio Loncomilla Center for Web Research Universidad de Chile

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Outline Motivation & Recognition Examples Dimensionality problems Object Recognition using Local Descriptors Matching & Storage of Local Descriptors Conclusions

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Motivation Object recognition approaches based on local invariant descriptors (features) have become increasingly popular and have experienced an impressive development in the last years. Invariance against: scale, in-plane rotation, partial occlusion, partial distortion, partial change of point of view. The recognition process consists on two stages: 1.scale-invariant local descriptors (features) of the observed scene are computed. 2.these descriptors are matched against descriptors of object prototypes already stored in a model database. These prototypes correspond to images of objects under different view angles.

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Recognition Examples (1/2)

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Recognition Examples (2/2)

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Image Matching Examples (1/2)

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Image Matching Examples (2/2)

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Some applications Object retrieval in multimedia databases (e.g. Web) Image retrieval by similarity in multimedia databases Robot self-localization Binocular vision Image alignment and matching Movement compensation …

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However … there are some problems Dimensionality problems A given image can produce ~100-1,000 descriptors of 128 components (real values) The model database can contain until 1,000-10,000 objects in some special applications => large number of comparisons => large processing time => large databases size Main motivation of this talk: To get some ideas about how to make efficient comparisons between local descriptors as well as efficient storage of them …

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Recognition Process The recognition process consists on two stages: 1.scale-invariant local descriptors (features) of the observed scene are computed. 2.these descriptors are matched against descriptors of object prototypes already stored in a model database. These prototypes correspond to images of objects under different view angles.

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Interest Points Detection Scale Invariant Descriptors (SIFT) Calculation Affine Transform Calculation SIFT Matching SIFT Database Interest Points Detection Scale Invariant Descriptors (SIFT) Calculation Reference Image Offline Database Creation Input Image Affine Transform Parameters

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Interest Points Detection Scale Invariant Descriptors (SIFT) Calculation Affine Transform Calculation SIFT Matching SIFT Database Interest Points Detection Scale Invariant Descriptors (SIFT) Calculation Input Image Affine Transform Parameters Reference Image Offline Database Creation

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Interest Points Detection (1/2) Interests points correspond to maxima of the SDoG (Subsampled Difference of Gaussians) Scale-Space (x,y, ). Scale Space SDoG Ref: Lowe 1999

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Interest Points Detection (2/2) Examples of detected interest points. Our improvement: Subpixel location of interest points by a 3D quadratic approximation around the detected interest point in the scale-space.

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Interest Points Detection Scale Invariant Descriptors (SIFT) Calculation Affine Transform Calculation SIFT Matching SIFT Database Interest Points Detection Scale Invariant Descriptors (SIFT) Calculation Input Image Affine Transform Parameters Reference Image Offline Database Creation

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SIFT Calculation For each obtained keypoint, a descriptor or feature vector that considers the gradient values around the keypoint is computed. This descriptors are called SIFT (Scale - Invariant Feature Transformation). SIFTs allow obtaining invariance against to scale and orientation. Ref: Lowe 2004

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Interest Points Detection Scale Invariant Descriptors (SIFT) Calculation Affine Transform Calculation SIFT Matching SIFT Database Interest Points Detection Scale Invariant Descriptors (SIFT) Calculation Input Image Affine Transform Parameters Reference Image Offline Database Creation

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SIFT Matching Euclidian distance between the SIFTs (vectors) is employed.

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Interest Points Detection Scale Invariant Descriptors (SIFT) Calculation Affine Transform Calculation SIFT Matching SIFT Database Interest Points Detection Scale Invariant Descriptors (SIFT) Calculation Input Image Affine Transform Parameters Reference Image Offline Database Creation

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Affine Transform Calculation (1/2) Several stages are employed: 1.Object Pose Prediction In the pose space a Hough transform is employed for obtaining a coarse prediction of the object pose, by using each matched keypoint for voting for all object pose that are consistent with the keypoint. A candidate object pose is obtained if at least 3 entries are found in a Hough bin. 2. Affine Transformation Calculation A least-squares procedure is employed for finding an affine transformation that correctly account for each obtained pose.

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Affine Transform Calculation (2/2) 3. Affine Transformation Verification Stages: Verification using a probabilistic model (Bayes classifier). Verification based on Geometrical Distortion Verification based on Spatial Correlation Verification based on Graphical Correlation Verification based on the Object Rotation 4. Transformations Merging based on Geometrical Overlapping In blue verification stages proposed by us for improving the detection of robots heads.

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Input Image Reference Images AIBO Head Pose Detection Example

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Matching & Storage of Local Descriptors Each reference image gives a set of keypoints. Each keypoint have a graphical descriptor, which is a 128- components vector. All the (keypoint,vector) pairs corresponding to a set of reference images are stored in a set T. Reference image x,y,n, v 1 v 2... v 128 x,y,n, v 1 v 2... v 128 x,y,n, v 1 v 2... v 128 x,y,n, v 1 v 2... v (1)(2)(3)(4) = T

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Reference image p1p1 d1d1 p2p2 d2d2 p3p3 d3d3 p4p4 d4d4... = T Matching & Storage of Local Descriptors More compact notation Each reference image gives a set of keypoints. Each keypoint have a graphical descriptor, which is a 128- components vector. All the (keypoint,vector) pairs corresponding to a set of reference images are stored in a set T.

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In the matching-generation stage, an input image gives another set of keypoints and vectors. For each input descriptor, the first and second nearest descriptors in T must be found. Then, a pair of nearest descriptors (d,d FIRST ) gives a pair of matched keypoints (p,p FIRST ). Matching & Storage of Local Descriptors Input image p d... Search in T p FIRST d FIRST p SEC d SEC p1p1 d1d1 p2p2 d2d2...

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The match is accepted if the ratio between the distance to the first nearest descriptor and the distance to the second nearest descriptor is lower than a given threshold This indicates that exists no possible confusion in the search results. Matching & Storage of Local Descriptors Accepted if: distance(, ) < * distance (, ) dd FIRST dd SEC

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A way to store the T set in a ordered way is using a kd-tree In this case, we will use a 128d-tree As well known, in a kd-tree the elements are stored in the leaves. The other nodes are divisions of the space in some dimension. Storage: Kd-trees 1 >2 2 >3 2 > All the vectors with more than 2 in the first dimension, stored at right side Division node Storage node

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Generation of balanced kd-trees: We have a set of vectors We calculate the means and variances for each dimension i. Storage: Kd-trees a1a2…a1a2… b1b2…b1b2… c1c2…c1c2… d1d2…d1d2… ………………

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Tree construction: Select the dimension i MAX with the largest variance Order the vectors with respect to the i MAX dimension. Select the median M in this dimension. Get a division node. Repeat the process in a recursive way. Storage: Kd-trees iMAX >M Nodes with i MAX component lesser than M Nodes with i MAX component greater than M

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Search process of the nearest neighbors, two alternatives: Compare almost all the descriptors in T with the given descriptor and return the nearest one, or Compare Q nodes at most, and return the nearest of them (compare calculate Euclidean distance) Requires a good search strategy It can fail The failure probability is controllable by Q We choose the second option and we use the BBF (Best Bin First) algorithm. Search Process

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Set: v: query vector Q: priority queue ordered by distance to v (initially void) r: initially is the root of T v FIRST : initially not defined and with an infinite distance to v ncomp: number of comparisons, initially zero. While (!finish): Make a search for v in T from r => arrive to a leaf c Add all the directions not taken during the search to Q in an ordered way (each division node in the path gives one not-taken direction) If c is more near to v than v FIRST, then v FIRST =c Make r = the first node in Q (the more near to v), ncomp++ If distance(r,v) > distance(v FIRST,v), finish=1 If ncomp > ncomp MAX, finish=1 Search Process: BBF Algorithm

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1 >2 2 > >7 1 > ?: queue: C MIN : Distance between 2 and 20 Search Example Requested vector 1 >2 18 I am a pointer 20>2 Go right Not-taken option 18

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Search Example 1 >2 2 > >7 1 > ?: C MIN : queue: 1 >2 2 > >7 Go right 18 1 comparisons: 0

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1 >2 2 > >7 1 > ?: queue: 1 >2 2 > >8 C MIN : Search Example >6 Go right comparisons: 0

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1 >2 2 > >7 1 > ?: queue: 1 >2 2 > >8 14 C MIN : We arrived to a leaf Store nearest leaf in C MIN Search Example comparisons: 1

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1 >2 2 > >7 1 > ?: queue: 1 >2 2 > >8 14 C MIN : Distance from best-in-queue is lesser than distance from c MIN Start new search from best in queue Delete best node in queue Search Example

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1 >2 2 > >7 1 > ?: queue: 1 > >8 12 C MIN : Go down from here Search Example comparisons: 1

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1 >2 2 > >7 1 > ?: queue: 1 > >8 12 C MIN : We arrived to a leaf Store nearest leaf in C MIN Search Example comparisons: 2

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1 >2 2 > >7 1 > ?: queue: 1 > >8 12 C MIN : Search Example Distance from best-in-queue is NOT lesser than distance from c MIN Finish comparisons: 2

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Conclusions BBF+Kd-trees: good trade off between short search time and high success probability. But, perhaps BBF+ Kd-trees is not the optimal solution. Finding a better methodology is very important to massive applications (as an example, for Web image retrieval)

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