nips nips2004 nips2004-40 knowledge-graph by maker-knowledge-mining

40 nips-2004-Common-Frame Model for Object Recognition

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Author: Pierre Moreels, Pietro Perona

Abstract: A generative probabilistic model for objects in images is presented. An object consists of a constellation of features. Feature appearance and pose are modeled probabilistically. Scene images are generated by drawing a set of objects from a given database, with random clutter sprinkled on the remaining image surface. Occlusion is allowed. We study the case where features from the same object share a common reference frame. Moreover, parameters for shape and appearance densities are shared across features. This is to be contrasted with previous work on probabilistic ‘constellation’ models where features depend on each other, and each feature and model have different pose and appearance statistics [1, 2]. These two differences allow us to build models containing hundreds of features, as well as to train each model from a single example. Our model may also be thought of as a probabilistic revisitation of Lowe’s model [3, 4]. We propose an efﬁcient entropy-minimization inference algorithm that constructs the best interpretation of a scene as a collection of objects and clutter. We test our ideas with experiments on two image databases. We compare with Lowe’s algorithm and demonstrate better performance, in particular in presence of large amounts of background clutter.

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 edu Abstract A generative probabilistic model for objects in images is presented. [sent-3, score-0.288]

2 Scene images are generated by drawing a set of objects from a given database, with random clutter sprinkled on the remaining image surface. [sent-6, score-0.492]

3 We study the case where features from the same object share a common reference frame. [sent-8, score-0.288]

4 Moreover, parameters for shape and appearance densities are shared across features. [sent-9, score-0.223]

5 This is to be contrasted with previous work on probabilistic ‘constellation’ models where features depend on each other, and each feature and model have different pose and appearance statistics [1, 2]. [sent-10, score-0.657]

6 We propose an efﬁcient entropy-minimization inference algorithm that constructs the best interpretation of a scene as a collection of objects and clutter. [sent-13, score-0.234]

7 We test our ideas with experiments on two image databases. [sent-14, score-0.206]

8 1 Introduction There is broad agreement in the machine vision literature that objects and object categories should be represented as collections of features or parts with distinctive appearance and mutual position [1, 2, 4, 5, 6, 7, 8, 9]. [sent-16, score-0.69]

9 faces) have been proposed by virtually all the cited authors, far fewer for recognition (list all objects and their pose in a given image) where matching would ideally take a logarithmic time with respect to the number of available models [3, 4]. [sent-19, score-0.346]

10 This work is based on two complementary efforts: the deterministic recognition system proposed by Lowe [3, 4], and the probabilistic constellation models by Perona and collaborators [1, 2]. [sent-21, score-0.267]

11 The ﬁrst line of work has three attractive characteristics: objects are represented with hundreds of features, thus increasing robustness; models are learned from a single training example; last but not least, recognition is efﬁcient with databases of hundreds of objects. [sent-22, score-0.326]

12 The drawback of Lowe’s approach is that both modeling decisions and algorithms rely on heuristics, whose design and performance may be far from optimal in Figure 1: Diagram of our recognition model showing database, test image and two competing hypotheses. [sent-23, score-0.336]

13 To avoid a cluttered diagram, only one partial hypothesis is displayed for each hypothesis. [sent-24, score-0.351]

14 The predicted position of models according to the hypotheses are overlaid on the test image. [sent-25, score-0.325]

15 Conversely, the second line of work is based on principled probabilistic object models which yield principled and, in some respects, optimal algorithms for learning and recognition/detection. [sent-27, score-0.209]

16 A major difference with the work described here lies in the probabilistic treatment of hypotheses, which allows us here to use directly hypothesis likelihood as a guide for the search, instead of the arbitrary admissible heuristic required by A*. [sent-32, score-0.259]

17 Each model is the set of features extracted from one training image of a given object - although this could be generalized to features from many images of the same object. [sent-35, score-0.658]

18 Models are indexed by k and denoted by mk , while indices i and j are used respectively for features extracted from the test image k and from model images: f i denotes the i − th test feature, while f j denotes the j − th feature from the k − th model. [sent-36, score-0.814]

19 The features extracted from model images (training set) form the database. [sent-37, score-0.3]

20 A feature detected in a test image can be a consequence of the presence of a model object in the image, in which case it should be associated to a feature from the database. [sent-38, score-0.614]

21 In the alternative, this feature is attributed to a clutter - or background - detection. [sent-39, score-0.329]

22 The geometric information associated to each feature contains position information (x and y coordinates, denoted by the vector x), orientation (denoted by θ) and scale (denoted by k k σ). [sent-40, score-0.343]

23 It is denoted by X i = (x, θi , σi ) for test feature f i and Xjk = (xk θj , σj ) for model j k feature fj . [sent-41, score-0.602]

24 This geometric information is measured relatively to the standard reference frame of the image in which the feature has been detected. [sent-42, score-0.413]

25 All features extracted from the same image share the same reference frame. [sent-43, score-0.343]

26 The appearance information associated to a feature is a descriptor characterizing the local image appearance near this feature. [sent-44, score-0.668]

27 The measured appearance information is denoted by k Ai for test feature f i and Ak for model feature f j . [sent-45, score-0.582]

28 In our experiments, features are detected j at multiple scales at the extrema of difference-of-gaussians ﬁltered versions of the image [4, 12]. [sent-46, score-0.285]

29 A partial hypothesis h explains the observations made in a fraction of the test image. [sent-48, score-0.467]

30 It combines a model image m h and a corresponding set of pose parameters X h . [sent-49, score-0.246]

31 This allows us to search in parallel for multiple objects in a test image. [sent-56, score-0.241]

32 A hypothesis H is the combination of several partial hypotheses, such that it explains completely the observations made in the test image. [sent-57, score-0.467]

33 A special notation H 0 or h0 denotes any (partial) hypothesis that states that no model object is present in a given fraction of the test image, and that features that could have been detected there are due to clutter. [sent-58, score-0.616]

34 Our objective is to ﬁnd which model objects are present in the test scene, given the observations made in the test scene and the information that is present in the database. [sent-59, score-0.45]

35 In probabilistic terms, we look for hypotheses H for which the likelihood ration LR(H) = k P (H|{fi },{fj }) k P (H0 |{fi },{fj }) > 1. [sent-60, score-0.216]

36 A key assumption of this work is that once the pose parameters of the objects (and thus their reference frames) are known, the geometric conﬁguration and appearance of the test features are independent from each other. [sent-63, score-0.787]

37 We also assume independence between features associated to models and features associated to clutter detections, as well as independence k k between separate clutter detections. [sent-64, score-0.776]

38 Assignment vectors v represent matches between features from the test scene, and model features or clutter. [sent-67, score-0.473]

39 The dimension of each assignment vector is the number of test features ntest . [sent-68, score-0.45]

40 Its i − th component v(i) = (k, j) denotes that the test feature f i is matched to k fv(i) = fj , j − th feature from model m k . [sent-69, score-0.645]

41 The set V H of assignment vectors compatible with a hypothesis H are those that assign test features only to models present in H (and to clutter). [sent-71, score-0.671]

42 In particular, the only assignment vector compatible with h 0 is v0 such that ∀i, v0 (i) = (0, 0). [sent-72, score-0.219]

43 We obtain   LR(H) = P (H) P (H0 ) k P (v|{fj }, mh , Xh ) · v∈VH h∈H i|fi ∈h P (fi |fv(i) , mh , Xh )  (2) P (fi |h0 ) k P (H) is a prior on hypotheses, we assume it is constant. [sent-73, score-0.43]

44 The term P (v|{f j }, mh , Xh ) is discussed in 3. [sent-74, score-0.215]

45 •P (fi |fv(i) , mh , Xh ) : fi and fv(i) are believed to be one and the same feature. [sent-76, score-0.469]

46 This noise probability p n encodes differences in appearance of the descriptors, but also in geometry, i. [sent-78, score-0.193]

47 position, scale, orientation Assuming independence between appearance information and geometry information, k pn (fi |fj , mh , Xh ) = pn,A (Ai |Av(i) , mh , Xh ) · pn,X (Xi |Xv(i) , mh , Xh ) (3) Figure 2: Snapshots from the iterative matching process. [sent-80, score-1.049]

48 Two competing hypotheses are displayed (top and bottom row) a) Each assignment vector contains one assignment, suggesting a transformation (red box) b) End of iterative process. [sent-81, score-0.381]

49 The correct hypothesis is supported by numerous matches and high belief, while the wrong hypothesis has only a weak support from few matches and low belief. [sent-82, score-0.6]

50 The error in geometry is measured by comparing the values observed in the test image, with the predicted values that would be observed if the model features were to be transformed according to the parameters X h . [sent-83, score-0.316]

51 3 Search for the best interpretation of the test image The building block of the recognition process is a question, comparing a feature from a database model with a feature of the test image. [sent-89, score-0.738]

52 A question selects a feature from the database, and tries to identify if and where this feature appears in the test image. [sent-90, score-0.355]

53 1 Assignment vectors compatible with hypotheses For a given hypothesis H, the set of possible assignment vectors V H is too large for explicit exploration. [sent-92, score-0.57]

54 In particular, each assignment vector v and each model referenced in v implies a set of pose parameters X v (extracted e. [sent-95, score-0.311]

55 Therefore, the term k P (v|{fj }, mh , Xh ) from (2) will be signiﬁcant only when X v ≈ Xh , i. [sent-98, score-0.215]

56 when the pose implied by the assignment vector agrees with the pose speciﬁed by the partial hypothesis. [sent-100, score-0.511]

57 (2) becomes LR(H) ≈ P (H) P (H0 ) h∈H i|fi ∈h P (fi |fvh (i) , mh , Xh ) P (fi |h0 ) (6) Our recognition system proceeds by asking questions sequentially and adding matches to assignment vectors. [sent-104, score-0.643]

58 It is therefore natural to deﬁne, for a given hypothesis H and the corresponding assignment vector v H and t ≤ ntest , the belief in vH by pn (ft |fv(t) , mht , Xht ) B0 (vH ) = 1, Bt (vH ) = · Bt−1 (vH ) (7) pbg (ft |h0 ) The geometric part of the belief (cf. [sent-105, score-0.949]

59 (3)-(5) characterizes how close the pose X v implied by the assignments is to the pose X h speciﬁed by the hypothesis. [sent-106, score-0.322]

60 The geometric component of the belief characterizes the quality of the appearance match for the pairs (f i , fv(i) ). [sent-107, score-0.485]

61 2 Entropy-based optimization Our goal is ﬁnding quickly the hypothesis that best explains the observations, i. [sent-109, score-0.276]

62 the hypothesis (models+poses) that has the highest likelihood ratio. [sent-111, score-0.197]

63 We compute such hypothesis incrementally by asking questions sequentially. [sent-112, score-0.267]

64 a given model is present in the image) as soon as the belief of a corresponding hypothesis exceeds a given conﬁdence threshold. [sent-116, score-0.296]

65 Therefore we approximate the MEE strategy with a simple heuristic: The next question consists of attempting to match one feature of the highest-belief model; speciﬁcally, the feature with best appearance match to a feature in the test image. [sent-126, score-0.889]

66 Questions to be examined are created by pairing database features to the test features closest in terms of appearance. [sent-129, score-0.437]

67 Note that since features encode location, orientation and scale, any single assignment between a test feature and a model feature contains enough information to characterize a similarity transformation. [sent-130, score-0.718]

68 It is therefore natural to restrict the set of possible transformations to similarities, and to insert each candidate assignment in the corresponding geometric hash table entry. [sent-131, score-0.509]

69 The set of hypotheses is initialized to the center of the hash table entries, and their belief is set to 1. [sent-133, score-0.349]

70 A partial hypothesis corresponds to a hash table entry, we consider only the candidate assignments that fall into this same entry. [sent-135, score-0.546]

71 The hypothesis H that currently has the highest likelihood ratio is selected. [sent-137, score-0.197]

72 1, only the best assignment Figure 3: Results from our algorithm in various situations (viewpoint change can be seen in Fig. [sent-140, score-0.22]

73 Each row shows the best hypothesis in terms of belief. [sent-142, score-0.241]

74 The threshold used is the repeatability rate deﬁned in [15] m vector is explored: if p n (fi |fj h , mh , Xh ) > pbg (fi ) the match is accepted and inserted in m the hypothesis. [sent-146, score-0.603]

75 In the alternative, f i is considered a clutter detection and f j h is a missed detection. [sent-147, score-0.248]

76 After adding an assignment to a hypothesis, frame parameters X h are recomputed using least-squares optimization, based on all assignments currently associated to this hypothesis. [sent-149, score-0.275]

77 This parameter estimation step provides a progressive reﬁnement of the model pose parameters as assignments are added. [sent-150, score-0.189]

78 The exploration of a partial hypothesis ends when no more candidate match is available in the hash table entry. [sent-153, score-0.603]

79 The search ends when all test scene features have been matched or assigned to clutter. [sent-155, score-0.357]

80 1 Experimental setting We tested our algorithm on two sets of images, containing respectively 49 and 161 model images, and 101 and 51 test images (sets P M − gadgets − 03 and JP − 3Dobjects − 04 available from http : //www. [sent-157, score-0.204]

81 Test images contained from zero (negative examples) to ﬁve objects, for a total of 178 objects in the ﬁrst set, and 79 objects in the second set. [sent-163, score-0.31]

82 A large fraction of each test image consists of background. [sent-164, score-0.206]

83 The objects were always moved between model images and test images. [sent-168, score-0.321]

84 The images of model objects used in the learning stage were downsampled to ﬁt in a 500 × 500 pixels box, the test images were downsampled to 800 × 800 pixels. [sent-169, score-0.469]

85 With these settings, the number of features generated by the features detector was of the order of 1000 per training image and 2000-4000 per test image. [sent-170, score-0.466]

86 A ground truth model was created by cutting a rectangle from the test image and adding noise. [sent-172, score-0.272]

87 The two rows show the best and second best model found by each algorithm (estimated frame position shown by the red box, features that found a match are shown in yellow). [sent-174, score-0.423]

88 In challenging situations with multiple objects or textured clutter, our method performs a more systematic check on geometric consistency by updating likelihoods every time a match is added. [sent-182, score-0.343]

89 Hypotheses starting with wrong matches due to clutter don’t ﬁnd further supporting matches, and are easily discarded by a threshold based on the number of matches. [sent-183, score-0.309]

90 Conversely, Lowe’s algorithm checks geometric consistency as a last step of the recognition process, but needs to allow for a large slop in the transformation parameters. [sent-184, score-0.206]

91 Spurious matches induced by clutter detections may still be accepted, thus leading to the acceptance of incorrect hypotheses. [sent-185, score-0.336]

92 5: the test image consists of a picture of concrete. [sent-187, score-0.206]

93 A rectangular patch was extracted from this image, noise was added to this patch, and it was inserted in the database as a new model. [sent-188, score-0.184]

94 With our algorithm, the best hypothesis found the correct match with the patch of concrete, its best contender doesn’t succeed in collecting more than one correspondence and is discarded. [sent-189, score-0.404]

95 In Lowe’s case, other models manage to accumulate a high number of correspondences induced by texture matches among clutter detections. [sent-190, score-0.303]

96 Both curves conﬁrm that our probabilistic interpretation leads to less false alarms than Lowe’s method for a same detection rate. [sent-195, score-0.201]

97 5 Conclusion We have proposed an object recognition method that combines the beneﬁts of a set of rich features with those of a probabilistic model of features positions and appearance. [sent-196, score-0.569]

98 The probabilistic model veriﬁes the validity of candidate hypotheses in terms of appearance and geometric conﬁguration. [sent-198, score-0.614]

99 Our system improves upon a state-of-the art recognition method based on strict feature matching. [sent-199, score-0.204]

100 In particular, the rate of false alarms in the presence Figure 6: Sample scenes and training objects from the two sets of images. [sent-200, score-0.196]

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