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94 nips-2006-Image Retrieval and Classification Using Local Distance Functions

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Author: Andrea Frome, Yoram Singer, Jitendra Malik

Abstract: In this paper we introduce and experiment with a framework for learning local perceptual distance functions for visual recognition. We learn a distance function for each training image as a combination of elementary distances between patch-based visual features. We apply these combined local distance functions to the tasks of image retrieval and classiﬁcation of novel images. On the Caltech 101 object recognition benchmark, we achieve 60.3% mean recognition across classes using 15 training images per class, which is better than the best published performance by Zhang, et al. 1

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 We learn a distance function for each training image as a combination of elementary distances between patch-based visual features. [sent-8, score-0.796]

2 We apply these combined local distance functions to the tasks of image retrieval and classiﬁcation of novel images. [sent-9, score-0.415]

3 3% mean recognition across classes using 15 training images per class, which is better than the best published performance by Zhang, et al. [sent-11, score-0.571]

4 1 Introduction Visual categorization is a difﬁcult task in large part due to the large variation seen between images belonging to the same class. [sent-12, score-0.248]

5 One of the more successful tools used in visual classiﬁcation is a class of patch-based shape and texture features that are invariant or robust to changes in scale, translation, and afﬁne deformations. [sent-19, score-0.365]

6 These include the Gaussian-derivative jet descriptors of [2], SIFT descriptors [3], shape contexts [4], and geometric blur [5]. [sent-20, score-0.599]

7 Then, (5) use distances between pairs of images as input to a learning algorithm, for example an SVM or nearest neighbor classiﬁer. [sent-24, score-0.372]

8 When given a test image, patches and features are extracted, distances between the test image and training images are computed, and a classiﬁcation is made. [sent-25, score-0.828]

9 The image on the left is a clear, color image of a cougar face. [sent-27, score-0.588]

10 As with most cougar face exemplars, the locations and appearances of the eyes and ears are a strong signal for class membership, as well as the color pattern of the face. [sent-28, score-0.298]

11 The image on the right shows the ears, eyes, and mouth, but due to articulation, the appearance of all have changed again, perhaps representing a common visual subcategory. [sent-31, score-0.293]

12 In most approaches, machine learning only comes to play in step (5), after the distances or similarities between training images are computed. [sent-33, score-0.405]

13 First, they would require representing each image as a ﬁxed-length feature vector. [sent-37, score-0.247]

14 The goal of this paper is to demonstrate that in the setting of visual categorization, it can be useful to determine the relative importance of visual features on a ﬁner scale. [sent-41, score-0.284]

15 In this work, we attack the problem from the other extreme, choosing to learn a distance function for each exemplar, where each function gives a distance value between its training image, or focal image, and any other image. [sent-42, score-0.911]

16 These functions can be learned from either multi-way class labels or relative similarity information in the training data. [sent-43, score-0.266]

17 The distance functions are built on top of elementary distance measures between patch-based features, and our problem is formulated such that we are learning a weighting over the features in each of our training images. [sent-44, score-0.668]

18 Using these local distance functions, we address applications in image browsing, retrieval and classiﬁcation. [sent-47, score-0.389]

19 In order to perform retrieval and classiﬁcation, we use an additional learning step that allows us to compare focal images to one another, and an inference procedure based on error-correcting output codes to make a class choice. [sent-48, score-0.853]

20 3% using only ﬁfteen exemplar images per category, which is an improvement over the best previously published recognition rate in [11]. [sent-51, score-0.503]

21 2 Distance Functions and Learning Procedure In this section we will describe the distance functions and the learning procedure in terms of abstract patch-based image features. [sent-52, score-0.352]

22 Any patch-based features could be used with the framework we present, and we will wait to address our choice of features in Section 3. [sent-53, score-0.295]

23 The training image for which a given learning problem is being solved will be referred to as its focal image. [sent-55, score-0.836]

24 In the rest of this section we will discuss one such learning problem and focal image, but keep in mind that in the full framework there are N of these. [sent-57, score-0.535]

25 We deﬁne the distance function we are learning to be a combination of elementary patch-based distances, each of which are computed between a single patch-based feature in the focal image F and a set of features in a candidate image I, essentially giving us a patch-to-image distance. [sent-58, score-1.435]

26 Any function between a patch feature and a set of features could be used to compute these elementary distances; we will discuss our choice in Section 3. [sent-59, score-0.47]

27 If there are M patches in the focal image, we have M patch-to-image distances to compute between F and I, and we notate each distance in that set as dF (I), where j ∈ [1, M ], and refer to the vector of these as dF (I). [sent-60, score-0.781]

28 The image-to-image j distance function D that we learn is a linear combination of these elementary distances. [sent-61, score-0.348]

29 Where wF is a vector of weights with a weight corresponding to each patch feature: M F wj dF (I) = wF · dF (I) j D(F, I) = (1) j=1 Our goal is to learn this weighting over the features in the focal image. [sent-62, score-0.809]

30 We set up our algorithm to learn from “triplets” of images, each composed of (1) the focal image F, (2) an image labeled “less similar” to F, and (3) an image labeled “more similar” to F. [sent-63, score-1.182]

31 This formulation has been used in other work for its ﬂexibility [7]; it makes it possible to use a relative ranking over images as training input, but also works naturally with multi-class labels by considering exemplars of the same class as F to be “more similar” than those of another class. [sent-64, score-0.56]

32 If we could use our learned distance function for F to rank these two images relative to one another, we ideally would want I d to have a larger value than I s , i. [sent-66, score-0.417]

33 Let xi = dF (I d ) − dF (I s ), the difference of the two elementary distance vectors for this triplet, now indexed by i. [sent-70, score-0.287]

34 For a given focal image, we will construct T of these triplets from our training data (we will discuss how we choose triplets in Section 5. [sent-72, score-1.086]

35 First, their triplets do not share the same focal image as they apply their method to learning one metric for all classes and instances. [sent-84, score-1.038]

36 This would 2 appear to preclude our use of patch features and more interesting distance measures, but as we show, this is an unnecessary restriction for the optimization. [sent-86, score-0.361]

37 3 Visual Features and Elementary Distances The framework described above allows us to naturally combine different kinds of patch-based features, and we will make use of shape features at two different scales and a rudimentary color feature. [sent-95, score-0.38]

38 Many papers have shown the beneﬁts of using ﬁlter-based patch features such as SIFT [3] and geometric blur [13] for shape- or texture-based object matching and recognition [14][15][13]. [sent-96, score-0.786]

39 We chose to use geometric blur descriptors, which were used by Zhang et al. [sent-97, score-0.323]

40 in [11] in combination with their KNN-SVM method to give the best previously published results on the Caltech 101 image recognition benchmark. [sent-98, score-0.415]

41 Like SIFT, geometric blur features summarize oriented edges within a patch of the image, but are designed to be more robust to afﬁne transformation and differences in the periphery of the patch. [sent-99, score-0.562]

42 In previous work using geometric blur descriptors on the Caltech 101 dataset [13][11], the patches used are centered at 400 or fewer edge points sampled from the image, and features are computed on patches of a ﬁxed scale and orientation. [sent-100, score-0.639]

43 We use two different scales of geometric blur features, the same used in separate experiments in [11]. [sent-102, score-0.323]

44 The larger has a patch radius of 70 pixels, and the smaller a patch radius of 42 pixels. [sent-103, score-0.262]

45 Our color features are histograms of eight-pixel radius patches also centered at edge pixels in the image. [sent-106, score-0.362]

46 Any “pixels” in a patch off the edge of the image are counted in a “undeﬁned” bin, and we convert the HSV coordinates of the remaining points to a Cartesian space where the z direction is value and (x, y) is the Cartesian projection of the hue/saturation dimensions. [sent-107, score-0.332]

47 These were the only parameters that we tested with the color features, choosing not to tune the features to the Caltech 101 dataset. [sent-109, score-0.245]

48 If we are computing the distance between the jth patch in the focal image to a candidate image I, we ﬁnd the closest feature of the same type in I using the L2 distance, and use that L2 distance as the jth elementary patch-toimage distance. [sent-112, score-1.566]

49 We only compare features of the same type, so large geometric blur features are not compared to small geometric blur features. [sent-113, score-0.918]

50 4 Image Browsing, Retrieval, and Classiﬁcation The learned distance functions induce rankings that could naturally be the basis for a browsing application over a closed set of images. [sent-115, score-0.333]

51 Consider a ranking of images with respect to one focal image, as in Figure 2. [sent-116, score-0.797]

52 Clicking on the sixth image shown would then take them to the ranking with that sunﬂower image as the focal image, which contains more sunﬂower results. [sent-118, score-0.984]

53 We also can make use of these distance functions to perform image retrieval: given a new image Q, return a listing of the N training images (or the top K) in order of similarity to Q. [sent-124, score-0.907]

54 If given class labels, we would want images ranked high to be in the same class as Q. [sent-125, score-0.289]

55 While we can use the N distance functions to compute the distance from each of the focal images Fi to Q, these distances are not directly comparable. [sent-126, score-1.113]

56 To address this in cases where we have multi-class labels, we do a second round of training for each focal image where we ﬁt a logistic classiﬁer to the binary (in-class versus out-of-class) training labels and learned distances. [sent-128, score-1.012]

57 Now, given a query image Q, we can compute a probability that the query is in the same class as each of the focal (training) images, and we can use these probabilities to rank the training images relative to one another. [sent-129, score-1.244]

58 The probabilities are on the same scale, and the logistic also helps to penalize poor focal rankings. [sent-130, score-0.589]

59 For each class, we sum the probabilities for all training images from that class, and the query is assigned to the class with the largest total. [sent-132, score-0.426]

60 Formally, if pj is the probability for the jth training image Ij , and C is the set of classes, the chosen class is arg maxC j:Ij ∈C pj . [sent-133, score-0.369]

61 This can be shown to be a relaxation of the Hamming decoding scheme for the error-correcting output codes in [17] in which the number of focal images is the same for each class. [sent-134, score-0.756]

62 This dataset has artifacts that make a few classes easy, but many are quite difﬁcult, and due to the important challenges it poses for scalable object recognition, it has up to this point been one of the de facto standard benchmarks for multi-class image categorization/object recognition. [sent-136, score-0.364]

63 The dataset contains images from 101 different categories, with the number of images per category ranging from 31 to 800, with a median of about 50 images. [sent-137, score-0.59]

64 We ignore the background class and work in a forced-choice scenario with the 101 object categories, where a query image must be assigned to one of the 101 categories. [sent-138, score-0.362]

65 [15]: we use varying numbers of training set sizes (given in number of examples per class), and in each training scenario, test with all other images in the Caltech101 dataset, except the BACKGROUND Google class. [sent-140, score-0.482]

66 This normalizes the overall recognition rate so that the performance for categories with a larger number of test images does not skew the mean recognition rate. [sent-142, score-0.576]

67 1 Training data The images are ﬁrst resized to speed feature computation. [sent-144, score-0.264]

68 We computed features for each of these images as described in Section 3. [sent-146, score-0.357]

69 We used up to 400 of each type of feature (two sizes of geometric blur and one color), for a maximum total of 1,200 features per image. [sent-147, score-0.546]

70 For images with few edge points, we computed fewer features so that the features were not overly redundant. [sent-148, score-0.518]

71 After computing elementary distances, we rescale the distances for each focal image and feature to have a standard deviation of 0. [sent-149, score-1.034]

72 Note that the training algorithm allows for a more nuanced training set where an image could be more similar with respect to one image and less similar with respect to another, but 3 You can also see retrieval rankings with probabilities at the web page. [sent-152, score-0.764]

73 We experimented with abandoning the max-margin optimization and just training a logistic for each focal image; the results were far worse, perhaps because the logistic was ﬁtting noise in the tails. [sent-153, score-0.694]

74 28 Figure 2: The ﬁrst 15 images from a ranking induced for the focal image in the upper-left corner, trained with 15 images/category. [sent-173, score-1.001]

75 Each image is shown with its raw distance distance, and only those marked with (pos) or (neg) were in the learning set for this focal image. [sent-174, score-0.861]

76 Instead of using the full pairwise combination of all in- and out-of-class images, we select triplets using elementary feature distances. [sent-180, score-0.461]

77 Thus, we refer to all the images available for training as the training set and the set of images used to train with respect to a given focal image as its learning set. [sent-181, score-1.375]

78 We want in our learning set those images that are similar to the focal image according to at least one elementary distance measure. [sent-182, score-1.247]

79 For each of the M elementary patch distance measures, we ﬁnd the top K closest images. [sent-183, score-0.39]

80 If all K images are in-class, then we ﬁnd the closest out-of-class image according to that distance measure and make K triplets with one out-of-class image and the K similar images. [sent-185, score-0.978]

81 The ﬁnal set of triplets for F is the union of the triplets chosen by the M measures. [sent-188, score-0.454]

82 On average, we used 2,210 triplets per focal image, and mean training time was 1-2 seconds (not including the time to compute the features, elementary distances, or choose the triplets). [sent-189, score-1.068]

83 2 Results We ran a series of experiments using all features, each with a different number of training images per category (either 5, 15, or 30), where we generated 10 independent random splits of the 8,677 images from the 101 categories into training and test sets. [sent-192, score-0.872]

84 We determined the C parameter of the training algorithm using leave-one-out cross-validation on a small random subset of 15 images per category, and our ﬁnal results are reported using the best value of C found (0. [sent-194, score-0.362]

85 In the 15 training images per category setting, we also performed recognition experiments on each of our features separately, the combination of the two shape features, and the combination of two shape features with the color features, for a total of ﬁve different feature combinations. [sent-198, score-1.255]

86 8% standard deviation)7 The next best performance was from the bigger geometric blur features with 49. [sent-201, score-0.459]

87 9%), followed by the smaller geometric blur features with 52. [sent-203, score-0.459]

88 Combining the two shape features together, we achieved 58. [sent-206, score-0.246]

89 7%), which 6 For big geometric blur, small geometric blur, both together, and color alone, the values were C=5, 1, 0. [sent-210, score-0.301]

90 Figure 3: Number of training exemplars versus average recognition rate across classes (based on the graph in [11]). [sent-214, score-0.33]

91 is better than the best previously published performance for 15 training images on the Caltech 101 dataset [11]. [sent-218, score-0.41]

92 Combining shape and color performed better than using the two shape features alone for 52 of the categories, while it degraded performance for 46 of the categories, and did not change performance in the remaining 3. [sent-219, score-0.465]

93 In Figure 4 we show the confusion matrix for combined shape and color using 15 training images per category. [sent-220, score-0.605]

94 Almost all the processing at test time is the computation of the elementary distances between the focal images and the test image. [sent-222, score-1.054]

95 In practice the weight vectors that we learn for our focal images are fairly sparse, with a median of 69% of the elements set to zero after learning, which greatly reduces the number of feature comparisons performed at test time. [sent-223, score-0.892]

96 8 After comparisons are computed, we only need to compute linear combinations and compare scores across focal images, which amounts to negligible processing time. [sent-225, score-0.57]

97 Acknowledgements We would like to thank Hao Zhang and Alex Berg for use of their precomputed geometric blur features, and Hao, Alex, Mike Maire, Adam Kirk, Mark Paskin, and Chuck Rosenberg for many helpful discussions. [sent-228, score-0.323]

98 Puzicha, “Shape matching and object recognition using shape contexts,” PAMI, vol. [sent-243, score-0.334]

99 Darrell, “Pyramic match kernels: Discriminative classﬁciation with sets of image features (version 2),” Tech. [sent-288, score-0.34]

100 Poggio, “Object recognition with features inspired by visual cortex,” in CVPR, 2005. [sent-320, score-0.316]

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