Large Scale Discovery of Spatially Related Images Ondřej Chum and Jiří Matas Center for Machine Perception Czech Technical University Prague

2 /26 Related Vision Problems Organize my holiday snapshots –Schaffalitzky and Zisserman ECCV’02 Find images containing a given “object” (“window”) –Sivic ICCV‘03, Nister CVPR‘06, Jegou CVPR’07, Philbin CVPR‘07, Chum ICCV’07 Find small “object” in a film –Sivic and Zisserman CVPR’04 Match and reconstruct Saint Marco –Snavely, Seitz and Szeliski SIGGRAPH’06 Find and match ALL spatially related images in a large database, using only visual information, i.e. not using (flicker) tags, EXIF info, GPS, …. This Work O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

3 /26 Visual Only Approach Large database ( images in our experiments) Find spatially related clusters Fast method, even for sizes up to 2 50 images Probability of successful discovery of spatial relation of images independent of database size O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

4 /26 Image Clustering and its Time Complexity Standard Approach (using image retrieval): Quadratic method in the size of database D -- O(D 2 ) the multiplicative constant at the quadratic term ~ 1 – quadratic even for small D 1.Take each image in turn 2.Use a image retrieval system to retrieve related images 3.Compute connected components of the graph Proposed method 1.Seed Generation – hashing characterize images by pseudo-random numbers stored in a hash table time complexity equal to the sum of variances of Poisson distributions linear for database size D ¼ Seed Growing – retrieval complete the clusters only for cluster members c << D, complexity O(cD) O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

5 /26 Building on Two Methods Fast (low recall) seed generation based on hashing Thorough (high recall) seed growing based on image retrieval Chum, Philbin, Isard, and Zisserman: Scalable Near Identical Image and Shot Detection CIVR 2007 Chum, Philbin, Sivic, Isard, and Zisserman: Total Recall: Automatic Query Expansion with a Generative Feature Model for Object Retrieval ICCV 2007 O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

6 /26 Image Representation Feature detector SIFT descriptor [Lowe’04] Visual vocabulary Vector quantization … Bag of words Set of words O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

7 /26 Hypothesizing Seeds with min-Hash A 1 ∩ A 2 A 1 U A 2 A1A1 A2A2 Image similarity measured as a set overlap (using min-Hash algorithm) Spatially related images share visual words Problem: Robustly estimate set overlap of high dimensional sparse binary vectors in constant time independent of the dimensionality (d ¼ 10 5 ) Set overlap probabilistically estimated via min-Hash Similar approach as LSH (locally sensitive hashing) O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

8 /26 min-Hash According to some (replicable) key select a small number of non-zero elements Similar vectors should have similar selected elements Key = generate a random number (a hash) for each dimension, choose nonzero element with minimal value of the key

9 /26 Seed Generation: Probability of Success An image pair forms a seed if at least one of k s-tuples of min-Hashes agrees. Probability that an image pair is retrieved is a function of the similarity: where s,k are user-controllable parameters of the method: s governs the size of the hashing table k is number of hashing tables Successfully retrieved pair of images = at least one collision in one of the tables (equivalent to AND-OR) O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

10 /26 Probability of Retrieving an Image Pair similarity (set overlap) Near duplicate Images Images of the same object and unrelated images 8.9 % (sim = 0.057) 5.1% (sim = 0.047) 13.9 % (sim = 0,066) 100% (sim = 0.746) 100% (sim = 0.322) 99.5% (sim = 0,217) probability of retrieval O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

11 /26 Spatially Related Images 18.9 % (sim = 0,074)5.1 % (sim = 0,047) similarity (set overlap) probability of retrieval (log scale) 13.9 % 8.9 % 5.1 % 9.8 % 7.2 % 8.9 % 13.9 % 16.3 % 10.7 %

12 /26 10% 7% 4% 5% 4% Seed Generation P (no seed) = 6% % %68.88 % O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

13 / % Seed Generation P (no seed) = %31.84 %1.94 % Resemblance to RANSAC Related image pair ~ an all inlier sample (there is no need to enumerate them all, one hit is sufficient) Probability of retrieving an image pair ~ fraction of inliers The number of related image pairs ~ how many times we can try O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

14 /26 At Least One Seed in Cluster cluster size P(no seed ) similarity = probability of retrieval 6.2% 10.4% 16.1% Estimate of the probability of failure plot against the size of the cluster assumption used in this plot: all images in the cluster are related O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

15 /26 backproject features Growing the Seed Application of Total Recall –Combining average query expansion and transitive closure –3D geometric constraint (not only affine transformation) –Tighter geometric constraints (10 pixel threshold) query enhanced query Average query expansion (from possibly multiple coplanar structures) Transitive closure crawl O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

16 /26 Summary of the Method Unknown structure min-Hash seeds x Spatial verification Query Expansion Rejected seed Missed cluster Seed Cluster skeleton Failed retrieval Images O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

17 /26 Experiment 1 Univ. of Kentucky Dataset [Nister & Stewenius] 2550 clusters of size 4 – very small clusters “partial” ground truth: “different” cluster share the same background How many clusters have at least one seed? CONTRAST – DIFFERENT TASK If we were looking for ALL results not ANY (seed) the standard retrieval measure on this dataset would be only 1.63 out of % O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

18 /26 Experimental Validation UKY dataset cluster size P(no seed) similarity = probability of retrieval 6.2% 10.4% 16.1% + In University of Kentucky dataset “average” similarity slightly above 0.06 O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

19 /26 Experimental Results on 100k Images Hertford Keble Magdalen Pitt Rivers Radcliffe Camera All Soul's Ashmolean Balliol Bodleian Christ Church Cornmarket Images downloaded from FLICKR Includes 11 Oxford Landmarks with manually labelled ground truth O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

20 /26 Experimental Results on 100k Images Settings scalable to millions images, also finding small clusters Settings scalable to billions images, only finding larger clusters Timing: 17 min 13 sec + 16 min 20 sec = sec / image O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

21 /26 Application – Object Labelling Factorizing the clusters using multiple constrains Matches between images Weak geometric constraints (coplanarity, disparity) Photographer’s psychology – tends to take pictures of single objects

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24 /26 Automatic 3D Reconstruction O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

25 /26 O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

26 /26 Conclusions Novel method for fast clustering in large collections Combines fast low recall method (seed generation) and thorough (total recall) method for seed growing Probability of finding a cluster rapidly increases with its size and is independent of the size of the database Can be incrementally updated as the database grows Efficient: sec / image on a single PC Fully parallelizable A state of the art near duplicate detection comes as a bonus (as a part of seed generation) O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

27 /26 Thank you! Thanks to Daniel Martinec, Michal Perďoch, James Philbin, Jakub Pokluda Technical Report available O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images