Hello neighbor: accurate object retrieval with k-reciprocal nearest neighbors

Transcription

1 Hello neighbor: aurate objet retrieval with -reiproal nearest neighbors Danfeng Qin Stephan Gammeter Luas Bossard Till Qua,2 Lu van Gool,3 ETH Zürih 2 Kooaba AG 3 K.U. Leuven {ind,gammeter,bossard,tua,vangool}@vision.ee.ethz.h Abstrat This paper introdues a simple yet effetive method to improve visual word based image retrieval. Our method is based on an analysis of the -reiproal nearest neighbor struture in the image spae. At uery time the information obtained from this proess is used to treat different parts of the raned retrieval list with different distane measures. This leads effetively to a re-raning of retrieved images. As we will show, this has two benefits: first, using different similarity measures for different parts of the raned list allows for ompensation of the urse of dimensionality. Seond, it allows for dealing with the uneven distribution of images in the data spae. Dealing with both hallenges has very benefiial effet on retrieval auray. Furthermore, a major part of the proess happens offline, so it does not affet speed at retrieval time. Finally, the method operates on the bag-of-words level only, thus it ould be ombined with any additional measures on e.g. either desriptor level or feature geometry maing room for further improvement. We evaluate our approah on ommon objet retrieval benhmars and demonstrate a signifiant improvement over standard bag-of-words retrieval.. Introdution We are interested in retrieving images showing a partiular objet from a large database of referene images. This is an important problem with appliations in Web image retrieval, mobile visual searh, or auto-annotation of photos. Typially, objet types overed by the images in the database onsist of landmar buildings, senery or other 3D objets. Most approahes to solve this problem are based on the visual words onept, whih in essene borrows tehniues from text retrieval, after uantizing loalized visual features into visual voabularies [6, 7, 2]. This method has turned out to be very powerful, sine it allows for salable retrieval in databases of millions of images at uite high preision. Even though astonishing progress has been made in terms of salability and preision, auray on ommon retrieval benhmars still shows room for signifiant improvements. And of ourse, any suh auray improvement should ideally not affet memory onsumption or retrieval time. Thus, many reent wors towards improving auray have foused on improving features, visual voabularies or distane measures on a uite general level. Beyond these rather general measures, a further vantage point for improvement is given by exploiting the speifi differenes between text and visual retrieval. For instane, in images we an exploit the geometri arrangement of visual features (in 2D or 3D), whereas in text douments we have only aess to the seuential arrangements of words in lines of text. Exploiting this geometri struture using RANSAC [9] or similar inds of estimations is onseuently a very ommon step taen in order to improve retrieval auray [7]. In this paper we try to exploit another harateristi speifi to visual data in order to improve auray of objet retrieval results: often, the referene database ontains many images showing the same objet overing it from varying viewpoints et. We mae use of this by onstruting a graph on the image database onneting eah image with liely related images. At uery time this graph is used to onstrut a set of database images that are losely related to the uery image, then based on this lose set the rest of the database is re-raned. As we will show this has two benefits: first, treating the two sets with different similarity measures allows for ompensation for the urse of dimensionality, i.e. the degradation of distane funtions in high dimensional spaes. Seond, it allows for dealing with the uneven distribution of images in the data spae. Dealing with both hallenges has very benefiial effet on retrieval auray. The main ontribution of this paper is a method that improves image retrieval purely on the bag-of-words level. It does so without relying on lower-level information lie for instane the geometri arrangement of features or the geometry of the desriptor spae. As suh our method an be used in a wide variety of settings. We also ahieve very ompetitive results at reasonable overhead in memory usage and very little additional omputational omplexity during 777

2 uery time. The remaining part of the paper is strutured as follows: We first disuss related wor in the immediately following setion. Setion 3 lies the basis for our method, by disussing some ey harateristis of visual words based objet retrieval. We introdue our method for more aurate objet retrieval in Setion 4. Experiments and analysis of the effets of optimization on retrieval tass follow in Setion 5. Setion 6 onludes the paper. 2. Related wor Our wor relates to reent ontributions in the field of objet retrieval with visual voabularies in several aspets. The relevant wors build on the ommon bag-of-features retrieval approah and have proposed improvements, whih an be roughly grouped into three ategories. A first group of wors deals with improvements on the feature level. In desriptor spae the Eulidian distane is often used to assess the similarity of features. However, it has been shown this is not the optimal similarity measure in most situations. In the ontext of large sale image retrieval this problem has reently been addressed by several wors. For instane in [5] a probabilisti relationship between visual words is proposed as an alternative distane measure. It is based on an oversegmentation of the desriptor spae with an extremely large voabulary, and probabilisti relations between the visual words. This way, for eah feature mapped to a visual word, a statisti of alternative visual words is learned. The relations are learned offline from a large set of feature tras. Slightly similar is the wor [9], where data is used to learn a projetion from SIFT feature spae to a new Eulidean spae, suh that lustering is more liely to put mathing desriptors into the same visual words. A seond group of wors deals with the uantization artifats introdued while assigning features to visual words. The most ommon effet of uantization artifats is, that for two images showing the same objet, orresponding features are not assigned to the same visual word. One way of dealing with this problem is by assigning eah feature desriptor to multiple visual words as proposed in [8], however the more words are assigned to a feature, the more posting lists in the inverted index have to be traversed, thus inreasing the uery time. In [], Jégou et al. addressed this problem by first onstruting a relatively oarse voabulary plus a binary signature for eah feature. When a feature of the uery images is assigned to a visual word of the oarse voabulary, the binary signature is used to filter out database features by setting a threshold on the Hamming distane. A third group of wors deals with shortomings on the doument retrieval or database level. In [7], Chum et al. adopt uery expansion (that originated in text retrieval) to the visual domain. Strit geometri verifiation is applied to the initial top list in order to extrat a set of images that are very liely to be relevant to the uery. Then a generative model is used to fuse the information provided by the additional images into a new uery, whih signifiantly inreases reall. A ommon ause of problems is due to the independene assumption between visual words, ommonly used beause of effiieny reasons. In reality this independene assumption is violated and some visual words o-our more often than others. This an severely degrade retrieval auray. If for instane the uery ontains a set of freuently o-ourring visual words, then it is liely to math to unrelated images that ontain the same set of o-ourring visual words. These sets are ommonly referred to as bursts [] or o-osets [6]. In [], Jégou et al. evaluated several voting shemes that aount for intra- and interimage bursts. Chum et al. [6] addressed this problem by finding and removing sets of freuently o-ourring visual words. In both ases improvement in retrieval auray was demonstrated. Also operating on the doument vetor level, Jégou et al. [2, 3] improved the auray of visual word retrieval, by aounting for hanges in the loal distributions of the visual word vetors. To this extent, they introdued an iterative update sheme that modifies the distane funtion between vetors in a way that nearest neighborhood relationships beome more symmetri. Most similar to this paper are probably [7] and [3]. As we will explain in the following setions in more detail, the ey differenes to our wor are that we do not rely on lower level information lie for instane the geometri arrangement of features and we do not symmetrize nearest neighbor relationships (in ontrast to [3]). 3. Motivation In this setion we motivate our approah for improving auray of objet retrieval by two ey observations. Before we disuss the observations we give a brief overview of objet retrieval with visual words. Overview of objet retrieval with visual words. In visual word based retrieval images are represented as sparse high dimensional visual word vetors. Given a uery vetor, visual searh is formulated as raning the vetors in the database aording to their distane or similarity to the uery vetor. These vetors are onstruted by first extrating a set of loal features (usually SIFT [4] or SURF [5] features) for a given image whih are then uantized using a visual voabulary. The visual voabulary is ommonly learned by lustering a random sample of feature desriptors, where the number of luster enters K is usually somewhere around 6. The uantization indies orrespond to the non zero elements of the visual word vetors. 778

3 sim(,d) ran Figure : Degradation of similarity in doument spae for a typial uery from the Oxford5 data set. The y-axis shows sim(, d), the x-axis the ran of retrieved images. The red irles show true positives at their similarity and ran. d sim(d,) sim(,a) Figure 2: Differene between the unidiretional nearest neighbor set top(2, ) and the 2-reiproal nearest neighbor set R(2, ). a b In the bag-of-words model, eah non zero element of the vetor ounts how many times the visual word appears in the image. Sine the number of visual words in an image is usually many orders of magnitude below the size of the visual voabulary, the visual word vetors are extremely sparse. Using an inverted index this sparsity is exploited to effiiently alulate the similarity of a uery vetor to all database vetors. For all experiments in this paper we use the same similarity funtion as [], whih orresponds to the bagof-words model with an additional inverse doument freueny weighting term: K i= sim (, d) = i d i idf(i) 2 () d ( K i= d D idf (i) = log d ) i d D d (2) i where and d are visual word vetors of length K and D = {d... d N } is the set of database vetors. Observation : Similariy funtions degrade uily in high dimensional spaes. A fundamental issue for visual word based image retrieval is the high dimensionality of the visual word vetor spae. While this high dimensionality failitates fast searh, it also has the effet, that most distane or similarity measures uily degenerate at points far away from the uery vetor. An illustration of this phenomenon is shown in Figure where we plot the similarity measure sim(, d) (.f. Euation ) for the top 7 raned images in the Oxford5 data set [2] for a given uery. Corretly retrieved mathes from the evaluation data set are denoted by a red irle. Most images with high similarity are of ourse true positives, however the similarity urve uily flattens out giving relevant and non relevant images almost the same sore at lower rans. So the similarity measure is very useful for images lose to the uery, but it loses its utility far away from the uery. One way of dealing with this problem is by modifying the similarity measure sim(, d) in a way that more relevant images are pushed loser to the uery and irrelevant images are pushed away from the uery. For instane, Hamming embedding [] or soft visual word assignment [8] do this by reduing uantization artifats. Desriptor spae learning tehniues [9, 5] push relevant images loser to the uery by orreting for the fat that the Eulidean norm is not a perfet distane measure in SIFT or SURF desriptor spaes. In addition, filtering irrelevant images from the raned lists is typially ahieved by geometri verifiation [7] or similar methods (e.g. []). In this paper we try to address these effets of the urse of dimensionality in a slightly different way. Aepting that the similarity measure an degrade uily, we will split the database vetors at uery time into two groups. One group whih is lose to the uery, and for whih the regular similarity measure sim(, d) an still orretly separate relevant from non-relevant vetors, and a seond group, for whih the similarity measure an not distinguish between relevant from non-relevant vetors anymore. For the seond group we use a different similarity measure. Observation 2: Non-reiproity of near neighbor relationships. Let us define the -nearest neighbors (i.e. the top- list) of a vetor as the most similar vetors in the database D: top(, ) D (3) top(, ) = (4) sim(, a) > sim(, b) a top(, ) b D \ top(, ) (5) While the similarity measure sim(, d) = sim(d, ) itself is symmetri, nearest neighbor relationships are not. This means that a top(, b) does not imply b top(, a) in general. We define the set of -reiproal nearest neighbors R(, a) of a as R(, a) = {b top(, a) a top(, b)} (6) 779

4 whih is of ourse trivially symmetri. The -reiproal nearest neighborhood relationship b R(, a) is also a muh stronger indiator of similarity than the unidiretional nearest neighborhood relationship b top(, a), sine it taes into aount the loal densities of vetors around a and b. We illustrate in Figure 2 the differene between the unidiretional nearest neighbor set top(2, ) and the 2reiproal nearest neighbor set R(2, ). top(2, ) ontains the node a and d, R(2, ) only ontains node d, even though a and d are at the same distane from the uery. In suh a situation it maes sense to assume that d is more relevant to the uery than a, sine a has a high similarity to other nodes that share no onnetion to. We are of ourse not the first to mae this observation. Contextual dissimilarity measures [2, 3] for instane are based on exatly this idea. However unlie [2, 3], we do not diretly symmetrize nearest neighborhood relationships in this wor. Instead we use -reiproal nearest neighbors as a tool to find images whih are very liely to be related and to disambiguate database vetors that are far away from the uery vetor. These two observations are the basis for our objet retrieval method, whih will be disussed in the following setion. = =96 top(,) R(,) Preision.8 Reall Figure 3: Preision and reall of R(, ) in omparison to the top(, ). We first define the forward ran f-ran(a, ) of a as the position that a has in the top list of and the baward ran b-ran(a, ) is defined as the position that oupies in the top- list of a: f-ran(a, ) = b-ran(a, ) = a R(, ) a top(, ) \ top(-, )(7) f-ran(, a) (8) f-ran(a, ) < b-ran(a, ) < (9) Sine we are only interested in finding nodes lose to the uery, we only onsider nodes d D if their forward and baward ran relative to the uery do not exeed a ertain threshold max : 4. Our Approah At uery time we want to separate the database into two disjoint sets, the lose set whih ontains images highly relevant to the uery and the far set whih simply refers to the rest of the database. The final raning list is the onatenation of the lose set for whih parts internally are raned aording to the original similarity measure sim(, d) (.f. Euation ) and the far set whih is raned aording do a different similarity measure. We first disuss how the lose set is onstruted and then desribe the similarity measure that is used for the far set. f-ran(, d) < max b-ran(, d) < max 2 () Ignoring all nodes whih do not satisfy these onstraints we grow N,t= by the following proedure as desribed in Algorithm. Algorithm : Expansion step Close set onstrution 4 5 In order to identify images highly related to the initial uery image, we start by adding the -reiproal nearest neighbors R(, ) of the uery to the lose set. In Figure 3 we show for a uery in the Oxford5 data set how preision and reall of R(, ) hange for various values of. With higher values of, reall is inreased and saturates while preision rarely dereases. Sine in pratie some images have very few -reiproal nearest neighbors, even for very large, we grow the initial lose set N,t= by iteratively adding neighboring nodes to inrease reall. Nodes are only added if a set of onditions are met whih are designed in a way, that only images that are very liely to be related to the uery image are added. 6 7 for t to 2 do N,t+ N,t ; foreah n N,t do if N,t R(, n) > 2 N,t then N,t+ R(, n) N,t+ ; if N,t R(, n) > R(, n) \ N,t then N,t+ R(, n) N,t+ ; The first ondition allows only nodes whih are onneted to at least half of the lose set to bring in their neighbors. This high onnetivity ensures that added nodes are very liely to be relevant to the uery. The seond ondition relaxes this restrition slightly by allowing wealy onneted nodes to bring in their neighbors if the amount of new neighbors is smaller than the amount of onnetions already made to the lose set. Nodes added to N,t+ are sorted aording to sim(, d) and inserted in this order into 78

5 b3 N,t b 2 n2 R(,) n3 3 2 n2 N,t+ n3 N,3 b b3 N,t b 2 b R(,) n b3 Figure 5: Example for the lose set in the expansion step. N,t+ n million images we have not evaluated this for the purpose of our method. At uery time the similarity of the uery image to all database images is alulated and the graph is updated to inlude a node for the uery image. b2 (b) Node C s neighborhood is onsidered, if it adds less unnown nodes than nown, i.e. N,t R(, ) > R(, ) \ N,t 4.2. Far set re-raning Figure 4: Overview over the expansion rules. For the new set N,t+ only nodes are onsidered whih either our in the first half of the top- list of the uery image ( n3 ), or if the uery image ours within the top list of the image (n ). One the lose set is onstruted, it is used to re-ran the rest of the database. Sine images outside of the lose set are liely to have a low similarity to the uery, the original similarity measure sim(, d) is not useful anymore. From the vantage point of the uery, images outside of the lose set all loo eually dissimilar. However if we turn the tables, and loo from the position of an element in the far set this might not be true. Images in the far set whih are losely surrounded by other images in the far set will populate their top(, ) list with their lose neighbors but not the ones from the lose set. However images whih are dissimilar to the entire database but still rather lose to the initial uery an populate their top(, ) list with images from the lose set. Intuitively it also maes sense that images whih do not have any lose neighbors exept for images in the lose set are more liely to be relevant to the uery, than images that have lose neighbors whih are not related to the lose set. In order to mae use of this ontextual similarity we alulate for eah doument in the far set (f D \ N,2 ) the average ran that images in the lose set would have if image f were used as a uery: the final lose set. This proedure an be seen as a form of uery expansion, however unlie [7] we do not rely on any geometri or other lower-level information. Figure 4 gives an overview of the two onditions for better visualization and in Figure 5 we give a real world example of the growing proedure. In order to effiiently onstrut the lose set for a new uery, we pre-ompute a direted graph (d... dn D, (u, v)i V ) on top of the image database. In this graph every node represents an image and a onnetion (u, v) V from node u to another node v is made if node v appears in the trunated top(max, ) list of u: (u, v) V v top(max, u) N,2 Query = (a) Node C s neighborhood is onsidered, if it ontains more than the half of the initial set, i.e. N,t R(, ) > 2 N,t N, n b N, n b () where we used max = for all experiments in this paper. Using Euations 8 and 9, -reiproal neighborhoods R(, ) an be effiiently determined. In order to onstrut this graph, we uery our retrieval system with every image in the database. While this step is uadrati in the number of images, we do not see this yet as a fundamental restrition sine omputation is trivially distributable. Also the uery operation is uite fast, for a set of one million images we ould ompute the aforementioned graph in less than 5 hours using only 8 mahines. It is reasonable to assume, that alulating the graph for million images would still be feasible. For larger data sets, approximations may be used lie for instane min hash [8] whih has only linear omplexity in the number of images. However sine we an still deal uite omfortably with up to one sim(f, ) =utoff (2) X min (b-ran(f, ), utoff) N,2 N,2 where we use a utoff to aount for the fat that only a trunated version of the raning lists is present at retrieval time. We used utoff = 3 for all experiments in this paper. 5. Experiments In this setion we evaluate the performane of our method on five different datasets. First we give an overview 78

6 of the datasets. Then we asses the performane of the lose set and the performane of the far set re-raning separately. At the end a omparison of our full method to the approah is given. 5.. Evaluated datasets We evaluated our method on the Oxford5 [7, 2], Oxford5 [7], Paris [8, 3], University of Kentuy [6, 4] and the INRIA Holidays [, ] dataset. Oxford5 and Paris are relatively small datasets ontaining 5 63 and 6 42 database images eah. For both datasets 55 ueries with ground truth are provided. In the Oxford dataset on average % of the database is relevant to a uery, whereas for the Paris dataset almost 3 % of images are relevant. Furthermore, there is a high variane in the number of ground truth images for the different ueries. The Kentuy dataset onsists of 2 images for whih always 4 show the same objet. The Holidays dataset onsists one million distrator images and 49 relevant images of whih 5 are ueries. For a large portion of the ueries in this dataset there are only or 2 relevant images. The Oxford5 dataset onsists of Oxford5 and distrator images. As we did not have aess to the original distrator images we downloaded random geotagged images from Flir and Panoramio 2 whih have been taen at least 5 m away from Oxford in order not to inorporate possibly relevant images that ould artifiially pollute the results. Furthermore we ensured that all downloaded images have resolutions between and pixels, as in the original Oxford5 dataset. We used Hessian Affine SIFT desriptors and approximate -means [7] to luster a visual voabulary with 5 entroids for Oxford5, Paris and Kentuy eah. For Oxford5 we used the same voabulary as for Oxford5. For the Holidays dataset we reeived the prealulated visual words for a 2 visual voabulary from the authors of []. Thus our and the one from [] are exatly the same. As performane measure, we used mean average preision (map) on the Oxford5, Oxford5, Paris and Holidays dataset while for the University of Kentuy dataset we use the top-4 sore as defined by [6] Close set auray In the first part we demonstrate, that the onstrution of the lose set whih forms the first part of the final raning list leads to higher auray than simply taing the top- elements of the original raning list. The size of the lose set for a given uery is dependent on the number of similar images in the database. Queries with many similar images in the database have a larger lose set than ueries with only few similar images in the database. Furthermore, the size of the lose set depends on the threshold. By varying we produe lose sets of different sizes. The far set for whih in this experiment regular raning (.f. Euation ) is used, is appended to the lose set to form the final raning list. As an be seen by the blue lines in Figures 6,7,8,9, this gives a major improvement on all datasets for a wide range of. The map and top-4 sore give high importane to the first part of a raning list, whih is exatly where the lose sets inreases auray Far set auray We investigate the effet of replaing the lose set by simply a trunated top- list for different values of and re-ran the far set using this list aording to Euation 2. As an be seen by the green lines in Figures 6,7,8,9, this gives an improvement on all datasets for small. However as inreases the performane asymptotially degrades ba to the base line, sine larger and larger portions of the beginning of the final raning list are raned using the same similarity measure as the. This is espeially visible for the Kentuy dataset. Sine the top-4 sore only onsiders the first 4 positions of the raning list, for > 4 the performane is eual to the Full method The full method ombines the aforementioned ran list onstrution methods, suh that the first entries of the final raning list onsist of the lose set to whih the far set is appended map Figure 6: Mean average preision for Paris. The red line in Figures 6,7,8,9, show the of the whole method for different thresholds. The ombination of lose set onstrution and far set re-raning leads to superior results over the in all ases. Figure shows the average preision for the versus the average preision of our improved method for individual uery images for a fixed = argmaxˆ map(ˆ). Off-diagonal marers in the upper left triangle show a performane improvement, marers in the lower right triangle 2 782

7 .85 map.44 map Figure 7: Mean average preision for Oxford5. Figure : Mean average preision for INRIA Holidays map new average preision new average preision average preision for average preision for (a) Oxford5 (b) Oxford5 Figure 8: Mean average preision for Oxford top-4 sore new average preision.2 average preision for new top-4 sore old top-4 sore 3.5 () Paris (d) Kentuy Figure 9: Top-4 sore for Kentuy. 2 Figure : Average preision (AP) of the versus AP of our method a degradation. For the University of Kentuy dataset a slightly different visualisation approah was taen. The top- 4 sore of the method is plotted against the top-4 sore of our new method. Eah of the bubble s area orresponds to the number of images at this oordinate. The ombination of both methods yields in all datasets to superior results over the. As the performane deays slowly, is not as dataset speifi as it might seem. Setting it to somewhere between 2 and 4 gives good results for real world datasets used in image retrieval appliations. As an be seen in Table for Oxford5, Oxford5 and Paris we ompete with the state of the art, however we do so without exploiting lower level information. For the Kentuy dataset we miss the state of the art only by. of top-4 preision. For the Holidays dataset it is well now that Hamming Embedding and Wea Geometri Consisteny Constraint an greatly improve results, further more the 2 visual voabulary is uite small for suh a large dataset. We hose to evaluate our method on this hallenging dataset to demonstrate that even under very unfavorable onditions we ahieve a signifiant improvement. Table 2 shows an overview over the total memory overhead per dataset and the average uery time overhead for eah uery. As for eah image in the database the forwardand the baward raning lists need to be stored, the memory overhead grows linearly with the database size. This overhead is in the same order of magnitude as for instane 783

8 Dataset Baseline Our method Jégou et al. Jégou et al. Miulí et al. Chum et al. Chum et al. Philbin et al. [3] [] [5] [7] [6] [9] Oxford5 [7, 2] Oxford5 [7] Paris [8, 3] INRIA+ Mio [, ] Kentuy [6, 4] Table : map for different datasets ompared to results of state of the art results. Dataset Oxford5 Oxford5 Paris INRIA Kentuy Memory [GiB] Avg. time [ms] Table 2: Additional memory overhead per dataset and average time overhead per uery. Hamming Embedding []. The uery time overhead is mainly dependent on the length of the baward raning list and the hosen threshold as this restrits the size of the lose and far set. 6. Conlusion We have demonstrated that a signifiant improvement in bag-of-words retrieval an be ahieved, without onsidering the geometri arrangement of features in an image nor by modifying the feature uantization step. Our method uses -reiproal nearest neighbors to identify an initial set of highly relevant images in the database whih are then used to re-ran the remaining part of the database. On many data sets our approah ompetes with the state of the art. The memory overhead of our method is linear in the number of douments while the average uery time overhead is negletable. As a seondary ontribution, we mae a binary exeutable and a C++ implementation of our our method available at our homepage 3. Additionally we publish the prealulated visual words for the Oxford5, Oxford5, Paris and Kentuy dataset together with an evaluation paage to reprodue our results at the same plae. Anowledgements We are grateful to Matthijs Douze for providing the visual words of the Holidays dataset and for the finanial support from the EC STREP projet IURO and the SNF projet K-Content. Referenes [] jegou/data. php. 3 [2] vgg/data/ oxbuildings/index.html. [3] vgg/data/ parisbuildings/index.html. [4] stewe/ubenh/. [5] H. Bay, T. Tuytelaars, and L. Van Gool. Surf: Speeded up robust features. In ECCV 6, 26. [6] O. Chum and J. Matas. Unsupervised disovery of oourrene in sparse high dimensional data. In CVPR, 2. [7] O. Chum, J. Philbin, J. Sivi, M. Isard, and A. Zisserman. Total reall: Automati uery expansion with a generative feature model for objet retrieval. In CVPR7, 27. [8] O. Chum, J. Philbin, and A. Zisserman. Near dupliate image detetion: min-hash and tf-idf weighting. 28. [9] M. A. Fishler and R. C. Bolles. Random sample onsensus: A paradigm for model fitting with appliations to image analysis and automated artography. In Comm. of the ACM, 98. [] H. Jégou, M. Douze, and C. Shmid. Hamming embedding and wea geometri onsisteny for large sale image searh. In ECCV8, 28. [] H. Jégou, M. Douze, and C. Shmid. On the burstiness of visual elements. In CVPR9, 29. [2] H. Jégou, H. Harzallah, and C. Shmid. A ontextual dissimilarity measure for aurate and effiient image searh. In CVPR 7, 27. [3] H. Jégou, C. Shmid, H. Harzallah, and J. Verbee. Aurate image searh using the ontextual dissimilarity measure. Trans. PAMI, 32():2, january 2. [4] D. G. Lowe. Objet reognition from loal sale-invariant features. In ICCV99, 999. [5] A. Miulí, M. Perdoh, O. Chum, and J. Matas. Learning a fine voabulary. In ECCV, 2. [6] D. Nistér and H. Stewénius. Salable reognition with a voabulary tree. In CVPR 6, 26. [7] J. Philbin, O. Chum, M. Isard, J. Sivi, and A. Zisserman. Objet retrieval with large voabularies and fast spatial mathing. In CVPR 7, 27. [8] J. Philbin, O. Chum, M. Isard, J. Sivi, and A. Zisserman. Lost in uantization: Improving partiular objet retrieval in large sale image databases. In CVPR8, 28. [9] J. Philbin, M. Isard, J. Sivi, and A. Zisserman. Desriptor learning for effiient retrieval. In ECCV, 2. [2] J. Sivi and A. Zisserman. Video google: a text retrieval approah to objet mathing in videos. In ICCV 3,