cvpr cvpr2013 cvpr2013-250 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Raghuraman Gopalan
Abstract: Estimating geographic location from images is a challenging problem that is receiving recent attention. In contrast to many existing methods that primarily model discriminative information corresponding to different locations, we propose joint learning of information that images across locations share and vary upon. Starting with generative and discriminative subspaces pertaining to domains, which are obtained by a hierarchical grouping of images from adjacent locations, we present a top-down approach that first models cross-domain information transfer by utilizing the geometry ofthese subspaces, and then encodes the model results onto individual images to infer their location. We report competitive results for location recognition and clustering on two public datasets, im2GPS and San Francisco, and empirically validate the utility of various design choices involved in the approach.
Reference: text
sentIndex sentText sentNum sentScore
1 com Abstract Estimating geographic location from images is a challenging problem that is receiving recent attention. [sent-4, score-0.249]
2 In contrast to many existing methods that primarily model discriminative information corresponding to different locations, we propose joint learning of information that images across locations share and vary upon. [sent-5, score-0.303]
3 We report competitive results for location recognition and clustering on two public datasets, im2GPS and San Francisco, and empirically validate the utility of various design choices involved in the approach. [sent-7, score-0.509]
4 [15]), which could either be noisy or missing depending on the location of interest, and application areas such as surveillance. [sent-11, score-0.195]
5 Most existing methods for location recognition follow the paradigm of discriminative modeling for feature selection and classification. [sent-13, score-0.335]
6 For instance, [11] used several lowlevel features that could distinguish images across locations and used a nearest-neighbor classifier to estimate query locations from a large data set. [sent-14, score-0.314]
7 While images in (a) correspond to familiar locations that either have distinct visual features or have good exposure amongst the general public, the location of images in (b) is hard to infer. [sent-16, score-0.386]
8 One intuitive way to address such cases is to analyze how those images are relatively similar to and different from other known locations so that a meaningful location estimate can be obtained. [sent-17, score-0.311]
9 We pursue such a goal in this work using tools pertaining to subspace geometry. [sent-18, score-0.291]
10 In addition to robust feature descriptors, there have been several studies on efficient schemes for classification and retrieval of location queries. [sent-22, score-0.195]
11 Scalable vocabulary tree coding algorithms were presented by [22, 13], while [ 16] modeled landmark image collections using iconic scene graphs. [sent-24, score-0.217]
12 Image features that are confusing from a place recognition perspective was studied by [14], and [5] addressed obtaining discriminative features that are geographically informative, while occurring frequently at the same time. [sent-25, score-0.336]
13 There have also been efforts that provide landmark search engines for web-scale image collections [32] and for mobile vision applications [3]. [sent-26, score-0.251]
14 Besides modeling location specific information, some studies have examined the utility of complimentary information provided by other data modalities. [sent-27, score-0.377]
15 7 7 7 3232 2 9 1 9 Discriminative approaches, however, do not entirely address an important problem in location recognition that is illustrated in Figure 1. [sent-29, score-0.228]
16 One feasible way to obtain an approximate location estimate of these images is tojointly analyze the properties they have in common to and vary from other well known locations. [sent-31, score-0.229]
17 Such an analysis should also account for the fact that the visual and location information of images do not always correlate for instance, one could have images that look very much alike but correspond to vastly different geographic areas. [sent-34, score-0.362]
18 We address this problem by pursuing a top-down approach where given a set of training images representative of different locations, we first group the images into dif- ferent domains based on location adjacency. [sent-35, score-0.865]
19 We then derive generative and discriminative subspaces of same dimensions from these domains, and motivated by [9], we model cross-domain transfer of similar (resp. [sent-36, score-0.692]
20 distinct) information by pursuing a Grassmann manifold interpretation of the space spanned by these generative (resp. [sent-37, score-0.3]
21 We finally embed the effect of this transformation onto images from training and query, and perform location inference in both recognition and clustering settings. [sent-39, score-0.346]
22 Now given a query image xt, the goal of this work is to estimate its location yt = f2 (f1(X)) where f1models information transfer across domains (that are created by grouping xi based on their location yi) and f2 denotes the subsequent classification or clustering mechanism. [sent-49, score-1.519]
23 Assigning images from X into domains D in a threelevel hierarchical manner, and organizing the domains into groups G for further analysis. [sent-75, score-1.212]
24 Each group contains four domains within which generative and discriminative subspaces are analyzed for cross-domain information transfer. [sent-76, score-1.343]
25 Such an analysis on groups in all three levels convey top-down information on how visually similar and distinct information looks like among image collections that trend progressively from global to local. [sent-77, score-0.329]
26 Modeling Cross-domain Information Transfer Creating Domains: Assuming that X correspond to images from all over the earth, we flatten the earth and create domains D in a three-level hierarchical fashion. [sent-80, score-0.655]
27 The first level domains D1 to D4 correspond to images from four quadrants (with each quadrant covering 90 degrees in latitude and 180 degrees in longitude) of the flattened earth, and let group G1 represent the collection all these four domains. [sent-81, score-0.846]
28 The second level domains D5 to D20 are obtained by splitting each first level domain into four quadrants, and we thus obtain four groups Gi = {Di}44∗∗i(i−1)+1,i = 2 to 5. [sent-82, score-0.798]
29 Similarly we obtain the third level domains D21 to D84 by splitting each of the second level domains into four quadrants, with which we constitute 16 groups. [sent-83, score-1.22]
30 So we have a total of c = 84 domains D = {Di}i8=41 that are split into 21 groups G = {Gi}i2=11 containing four domains each, which represents image collections pertaining to location neighborhoods that trend progressively from global to local. [sent-85, score-1.617]
31 We now model how visually similar and different information transform across domains within each group Gi. [sent-86, score-0.764]
32 We perform PCA on each domain Di to obtain a d N orthonormal matrix whose column space denotes the generative subspace Si1. [sent-89, score-0.43]
33 We obtain discriminative subspace pertaining to each Di by considering a one-vs. [sent-90, score-0.316]
34 other three domains in the group that Di belongs to) and performing a two-class PLS to obtain a d N orthonormal matrix whose column space correspond to the discriminative subspace Si2. [sent-93, score-1.019]
35 Let S = {Si1}i8=41 ∪ {Sj2}8j4=1 refer to the collection of generative and discriminative subspaces obtained from G. [sent-95, score-0.629]
36 The problem of modeling cross-domain information now translates into: (i) analyzing the space of these N-dimensional subspaces in Rd to study the transfer of visually generic (resp. [sent-96, score-0.566]
37 discriminative) subspaces within each group Gi, and (ii) embedding this information transfer onto each individual training data xi to obtain a new representation f1(xi) that is cognizant of the cross-domain variations. [sent-98, score-0.714]
38 Grassmann Manifold: Before starting our analysis, we note that the space of subspaces is non-Euclidean, and it can be characterized by the Grassmann manifold [6]. [sent-99, score-0.401]
39 The Grassmannian Gd,N is an analytical manifold which is the space of all N-dimensional subspaces in containing the origin. [sent-100, score-0.401]
40 1 Analyzing Information Flow Between Subspaces We first learn how information transforms across different domains within a group. [sent-106, score-0.646]
41 For this we consider a pair of generative (or discriminative) subspaces in that group, although the following analysis can be extended beyond a pair of subspaces. [sent-107, score-0.522]
42 S1 and S2 could either correspond to a pair of generative subspaces Si1 and Sj1 within a group, or a pair of discriminative subspaces Si2 and Sj2 within a group. [sent-110, score-1.013]
43 In our analysis we have 6 pairs of generative and 6 pairs of discriminative subspaces within each group (since a group has four domains), thereby making 12∗ 21 subspace pairs in all. [sent-111, score-1.001]
44 While one could consider a pair made of a generative subspace Si1 and a discriminative subspace Sj2, we did not pursue that since the information contained in such a pair is different. [sent-112, score-0.624]
45 Now to obtain the geodesic flow between S1 and S2, we compute the direction matrix A such that the geodesic along that di- × rection, while starting from S1, reaches S2 in unit time. [sent-122, score-0.264]
46 Using the information contained in A, we can ‘sample’ points along the geodesic to understand how information transforms between different domains. [sent-124, score-0.239]
47 denote the number of subspaces obtained from a geodesic, which includes S1, S2 and all intermediate subspaces sampled between them. [sent-129, score-0.704]
48 This process, when repeated between all pairs of generative (resp. [sent-130, score-0.205]
49 2 Embedded Data Representation We then embed this information onto the training data by projecting each xi on all c1 subspaces to result in a matrix Mi? [sent-137, score-0.575]
50 By repeating the above process for the entire training set X, we obtain n points on GN,N1 having location information yi associated with them. [sent-145, score-0.286]
51 Performing Location Inference We now train a classifier f2 by performing statistics over the point cloud f1(xi)’s on GN,N1 , to recognize location yt of the query xt. [sent-148, score-0.395]
52 However since the number of locations m is generally much higher than the amount of data available at each location, we discriminate between the domains instead. [sent-155, score-0.656]
53 = 64 domains from third level since they provide the finest location grouping of images xi among all the three levels of the hierarchy (Sec 2. [sent-157, score-0.919]
54 The query location yt is then inferred by first computing the matrix Mt from xt using the procedure described in Sec 2. [sent-161, score-0.423]
55 training data xi from four unique locations yi (m = 4; a specific mountain, wetland, city, desert) into three domains D (c = 3). [sent-166, score-0.845]
56 These domains may contain visually dissimilar images as we do only a coarse grouping. [sent-167, score-0.635]
57 Assume these three domains are combined into a single group G. [sent-168, score-0.631]
58 Step 2: Obtaining generative (red) and discriminative (green) subspaces from these domains, and sampling points (yellow) along the geodesic between them (solid and dashed lines, resp. [sent-169, score-0.744]
59 Step 3: Projecting each training data xi onto these subspaces to obtain an embedded representation f1(xi) - colored ovals (based on yi): black-city, orange-wetland, white-mountain, purple-desert. [sent-171, score-0.55]
60 Step 4: Learning a discriminative space f2 using Algo 3 (red ellipses) on f1(xi) grouped by their domains (c? [sent-172, score-0.681]
61 = c here), to infer location yt of f1(xt) (brown oval) derived from query xt. [sent-173, score-0.391]
62 and finally selecting the location yi of the nearest neighbor from Ftrain. [sent-174, score-0.278]
63 1 Clustering Besides location ‘recognition’, there could be cases where the data is not labeled. [sent-178, score-0.195]
64 Experiments We evaluate the method on two datasets, im2GPS [11], and San Francisco [3], for location recognition and clustering and present an analysis of relative merits of some design choices involved in our approach. [sent-202, score-0.365]
65 We created domains D using the procedure outlined in Section 2. [sent-213, score-0.61]
66 1, then modeled cross-domain information transfer using the geometry of subspaces derived from the domains (Sec 2. [sent-214, score-1.031]
67 = 64 domains with which the query location was inferred. [sent-220, score-0.889]
68 We then repeated the above process but with the classifier f2 trained on even finer domains, by first splitting each of the 64 domains vertically into two (c? [sent-223, score-0.655]
69 Observations: It can be seen that our method performs better overall, even by using only two features (out of the original seven), which shows the utility of the joint generative and discriminative information captured by our model. [sent-228, score-0.459]
70 Another observation is that the recognition improves with finer grouping of domains, which is intuitive since such domains are more representative of finer locations. [sent-230, score-0.758]
71 In Figure 5(c) we report the location recognition performance on two other test sets, 2K random and geographically uniform, that are provided as a part of the im2GPS dataset. [sent-231, score-0.386]
72 Utility of hierarchical formation of domains, and creating groups from them: We now study two alternate strategies to create and analyze domains D as opposed to the scheme discussed in Sec 2. [sent-233, score-0.672]
73 In the first setting we do not pursue a hierarchical scheme and use just the domains from the third level along with their grouping. [sent-235, score-0.615]
74 So we have 64 domains {Di}i8=421 that are consolidated into 16 groups {Gi}i2=15 (from Sec 2. [sent-236, score-0.638]
75 We then create generative and discriminative subspaces to analyze geodesics between as described earlier. [sent-238, score-0.697]
76 (b) Similar trends are observed in the location retrieval of query images on the default test set. [sent-246, score-0.346]
77 Results with 64 and 128 domains on these two test sets are given in the supplementary material. [sent-249, score-0.608]
78 It can be seen that the famous locations (top two rows) have retrievals that are both visually and geographically similar, while the retrievals for rows 4 and 5 are visually similar but geographically varying. [sent-253, score-0.66]
79 information from Case-A1 and consider generative and discriminative subspace pairs among all 64 domains. [sent-255, score-0.466]
80 Discriminative subspaces in the case are obtained by a twogroup class PLS in a one-vs-remaining(63 domains) setting. [sent-256, score-0.352]
81 We have 4032 subspace pairs in this case (64C2 each for generative pairs and discriminative pairs). [sent-257, score-0.459]
82 This suggests that a top-down mechanism of obtaining domains is better, and for analyzing subspaces across domains it is important to have some supervision (in terms of groups Gi) in modeling visual properties across locations. [sent-262, score-1.71]
83 Case-A1 and A2 deal with the domain and group creation aspect, whereas Case-B 1and B2 deal with obtaining the embedded representation f1(xi) using Euclidean tools instead of geometry-driven ones. [sent-268, score-0.234]
84 Utility of considering column space of Mi to perform location recognition: We then address the utility of obtaining the embedded cross-domain representation f1(xi) by considering the column span of matrix Mi. [sent-270, score-0.518]
85 1 Clustering We then performed a clustering experiment to account for cases where the data xi may not have location information yi. [sent-283, score-0.406]
86 We first created 64 random groupings of the data into domains D. [sent-285, score-0.61]
87 We then modeled cross-domain information by projecting each data xi ∈ X onto the geodesic between these subspaces to obtain f1(xi), and performed k-means clustering (Sec 2. [sent-287, score-0.726]
88 We computed the geolocation error for each xi by picking out four closest neighbors of f1(xi) from its cluster (using d¯2), computing the error between the ‘ground truth’ location yi with the ground truth location of its four neighbors, and taking the average of those four values. [sent-290, score-0.692]
89 While the clustering accuracy is not very high, we are still able to infer approximate locations without any labeled data, for a problem where visually similar images can come from vastly different locations. [sent-292, score-0.284]
90 We then created domains D and the corresponding groups G by partitioning the rectangular grid covering the city. [sent-298, score-0.674]
91 We then learnt f1 and f2 from the procedure described before to infer the locations of the test set containing 803 query images. [sent-300, score-0.234]
92 When the GPS option is used, we infer query location by computing nearest neighbors (Algorithm 3) from the training data pertaining to the domain of the query (obtained from its ground truth) and to the four domains adjacent to it. [sent-302, score-1.291]
93 Conclusion We proposed a top-down approach to jointly model generative and discriminative information portrayed by the data and demonstrated its utility for the challenging problem of location recognition and clustering, where the visual and location properties of images may not always correlate. [sent-308, score-0.882]
94 The competitive results obtained on two public datasets, along with an empirical analysis on the utility of certain design choices, seems to suggest the importance of modeling tools that are cognizant of the underlying geometric space of the data they operate on. [sent-309, score-0.267]
95 Visual word based location recognition in 3d models using distance augmented weighting. [sent-364, score-0.228]
96 (b) For every image, we compute the difference of its ‘ground truth’ location with the ground truth location of its four nearest neighbors, and consider the average ofthese location errors. [sent-401, score-0.66]
97 The k-means clustering and the corresponding random grouping of data into domains D was repeated 10 times and the average location errors are plotted. [sent-402, score-0.89]
98 Results using 64 and 128 domains are given in the supplementary material. [sent-407, score-0.608]
99 Modeling and recognition of landmark image collections using iconic scene graphs. [sent-437, score-0.25]
100 Joint people, event, and location recognition in personal photo collections using cross-domain context. [sent-456, score-0.3]
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