nips nips2003 nips2003-53 knowledge-graph by maker-knowledge-mining

53 nips-2003-Discriminating Deformable Shape Classes

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Author: Salvador Ruiz-correa, Linda G. Shapiro, Marina Meila, Gabriel Berson

Abstract: We present and empirically test a novel approach for categorizing 3-D free form object shapes represented by range data . In contrast to traditional surface-signature based systems that use alignment to match speciﬁc objects, we adapted the newly introduced symbolic-signature representation to classify deformable shapes [10]. Our approach constructs an abstract description of shape classes using an ensemble of classiﬁers that learn object class parts and their corresponding geometrical relationships from a set of numeric and symbolic descriptors. We used our classiﬁcation engine in a series of large scale discrimination experiments on two well-deﬁned classes that share many common distinctive features. The experimental results suggest that our method outperforms traditional numeric signature-based methodologies. 1 1

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Our approach constructs an abstract description of shape classes using an ensemble of classiﬁers that learn object class parts and their corresponding geometrical relationships from a set of numeric and symbolic descriptors. [sent-8, score-0.898]

2 1 1 Introduction Categorizing objects from their shape is an unsolved problem in computer vision that entails the ability of a computer system to represent and generalize shape information on the basis of a ﬁnite amount of prior data. [sent-11, score-0.587]

3 As pointed out in [10], how to construct a quantitative description of shape that accounts for the complexities in the categorization process is currently unknown. [sent-13, score-0.296]

4 However, only a handful of studies have addressed the problem of categorizing shapes classes containing a signiﬁcant amount of shape variation and missing information frequently found in real range scenes. [sent-19, score-0.481]

5 [9] developed a shape representation to match similar objects. [sent-21, score-0.263]

6 The so-called shape distribution encodes the shape information of a complete 3-D object as a probability distribution sampled from a shape function. [sent-22, score-0.864]

7 [1] extended the work on shape distribution by developing a representation of shape for object retrieval. [sent-25, score-0.601]

8 The representation is based on a spherical harmonics expansion of the points of a polygonal surface mesh rasterized into a voxel grid. [sent-30, score-0.755]

9 developed a physical model for studying neuropathological shape deformations using Principal Component Analysis and a Gaussian quadratic classiﬁer. [sent-33, score-0.263]

10 In [10], we developed a shape novelty detector for recognizing classes of 3-D object shapes in cluttered scenes. [sent-36, score-0.71]

11 The detector learns the components of a shapes class and their corresponding geometric conﬁguration from a set of surface signatures embedded in a Hilbert space. [sent-37, score-1.108]

12 The numeric signatures encode characteristic surface features of the components, while the symbolic signatures describe their corresponding spatial arrangement. [sent-38, score-1.7]

13 The encouraging results obtained with our novelty detector motivated us to take a step further and extend our algorithm to accommodate classiﬁcation by developing a 3-D shape classiﬁer to be described in the next section. [sent-39, score-0.458]

14 We were also motivated by applications in medical diagnosis and human interface design where 3-D shape information plays a signiﬁcant role. [sent-41, score-0.364]

15 2 Our Approach We develop our shape classiﬁer in this section. [sent-47, score-0.263]

16 The ﬁrst module processes numeric surface signatures and the second, symbolic ones. [sent-52, score-1.34]

17 These shape descriptors characterize our classes at two different levels of abstraction. [sent-53, score-0.414]

18 1 Surface signatures The surface signatures developed by Johnson and Hebert [5] are used to encode surface shape of free form objects. [sent-55, score-1.872]

19 In contrast to the shape distributions and harmonic descriptors, their spatial scale can be enlarged to take into account local and non-local effects, which makes them robust against the clutter and occlusion generally present in range data. [sent-56, score-0.375]

20 Experimental evidence has shown that the spin image and some of its variants are the preferred choice for encoding surface shape whenever the normal vectors of the surfaces of the objects can be accurately estimated [11]. [sent-57, score-0.825]

21 The symbolic signatures developed in [10] are used at the next level to describe the spatial conﬁguration of labeled surface regions. [sent-58, score-1.067]

22 A spin-image [5] is a two-dimensional histogram computed at an oriented point P of the surface mesh of an object (see Figure 1). [sent-60, score-0.82]

23 Contributing points are those that are within a speciﬁed distance of P and for which the surface normal forms an angle of less than the speciﬁed size with the surface normal N of P . [sent-62, score-0.904]

24 We use spin images as the numeric signatures in this work. [sent-66, score-0.768]

25 2) are somewhat related to numeric surface signatures in that they also start with a point P on the surface mesh and consider a set of contributing points Q, which are still deﬁned in terms of the distance from P and support angle. [sent-68, score-1.86]

26 The main difference is that they are derived from a labeled surface mesh (shown in Figure 2a); each vertex of the mesh has an associated symbolic label referencing a surface region or component in which it lies. [sent-69, score-1.817]

27 For symbolic surface signature construction, the vector P Q in Figure 2b is projected to the tangent plane at P where a set of orthogonal axes γ and δ have been deﬁned. [sent-72, score-0.599]

28 The resultant array is the symbolic surface signature at point P . [sent-79, score-0.646]

29 Figure 2: The symbolic surface signature for point P on a labeled surface mesh model of a human head. [sent-82, score-1.436]

30 2 Classifying shape classes We consider the classiﬁcation task for which we are given a set of l surface meshes C = {C1 , · · · , Cl } representing two classes of object shapes. [sent-85, score-0.958]

31 The problem is to use the given meshes and the labels to construct an algorithm that predicts the label y of a new surface mesh C. [sent-87, score-0.896]

32 We let C+1 (C−1 ) denote the shape class labeled with y = +1 (y = −1, respectively). [sent-88, score-0.408]

33 This can be achieved by using a morphable surface models technique such as the one described in [10]. [sent-90, score-0.334]

34 Finding shape class components Before shape class learning can take place, the salient feature components associated with C+1 and C−1 must be speciﬁed . [sent-91, score-0.806]

35 Each component of a class is identiﬁed by a particular region located on the surface of the class members. [sent-92, score-0.616]

36 For each class C+1 and C−1 the components are constructed one at a time using a region growing algorithm. [sent-93, score-0.271]

37 This algorithm iteratively constructs a classiﬁcation function (novelty detector), which captures regions in the space of numeric signatures S that approximately correspond to the support of an assumed probability distribution function FS associated with the class component under consideration. [sent-94, score-0.874]

38 In this context, a shape class component is deﬁned as the set of all mesh points of the surface meshes in a shape class whose numeric signatures lie inside of the support region estimated by the classiﬁcation function. [sent-95, score-2.44]

39 Figure 3: The component R was grown around the critical point p using the algorithm described in the text. [sent-97, score-0.294]

40 The numeric signatures for the critical point p of ﬁve of the models are also shown. [sent-99, score-0.816]

41 Their image width is 70 pixels and its region of inﬂuence covers about three quarters of the surface mesh models . [sent-100, score-0.775]

42 The input of this phase is a set of surface meshes that are samples of an object class Cy . [sent-102, score-0.672]

43 Select a set of critical points on a training object for class Cy . [sent-104, score-0.341]

44 Note that the critical points chosen for class C+ can differ from the critical points chosen for class C− . [sent-107, score-0.47]

45 For each critical point p of a class Cy , compute the numeric signatures at the corresponding points of every training instance of Cy ; this set of signatures is the training set Tp,y for critical point p of class Cy . [sent-111, score-1.664]

46 For each critical point p of class Cy , train a component detector (implemented as a ν-SVM novelty detector [12]) to learn a component about p, using the training set T p,y . [sent-113, score-0.708]

47 The component detector will actually grow a region about p using the shape information of the numeric signatures in the training sample. [sent-114, score-1.208]

48 Using the classiﬁer for point p, perform an iterative component growing operation to expand the component about p. [sent-118, score-0.273]

49 Figure 3 shows an example of a component grown by this technique about critical point p on a training set of 200 human faces from the University of South Florida database. [sent-128, score-0.397]

50 At the end of step I, there are my component detectors, each of which can identify the component of a particular critical point of the object shape class Cy . [sent-129, score-0.731]

51 That is, when applied to a surface mesh, each component detector will determines which vertices it thinks belong to its learned component (positive surface points), and which vertices do not. [sent-130, score-0.971]

52 The input of this step is the training set of numeric signatures and their corresponding labels for each of the m = m+1 + m−1 components. [sent-132, score-0.714]

53 The output is a component classiﬁer (multi-class νSVM) that, when given a positive surface point of a surface mesh previously processed with the bank of component detectors, will determine the particular component of the m components to which this point belongs. [sent-134, score-1.465]

54 Learning spatial relationships The ensemble of component detectors and the component classiﬁer described above deﬁne our classiﬁcation module mentioned at the beginning of the section. [sent-135, score-0.478]

55 A central feature of this module is that it can be used for learning the spatial conﬁguration of the labeled components just by providing as input the set C of training surface meshes with each vertex labeled with the label of its component or zero if it does not belong to a component. [sent-136, score-1.079]

56 The algorithm proceeds in the same fashion as described above except that the classiﬁers operate on the symbolic surface signatures of the labeled mesh. [sent-137, score-1.039]

57 The signatures are embedded in a Hilbert space by means of a Mercer kernel that is constructed as follows. [sent-138, score-0.482]

58 Since symbolic surface signatures are deﬁned up to a rotation, we use the virtual SV method for training all the classiﬁers involved. [sent-144, score-1.018]

59 The method consists of training a component detector on the signatures to calculate the support vectors. [sent-145, score-0.699]

60 Finally, the novelty detector used by the algorithm is trained with the enlarged data set consisting of the original training data and the set of virtual support vectors. [sent-148, score-0.325]

61 The worse case complexity of the classiﬁcation module is O(nc2 s), where n is the number of vertices of the input mesh, s is the size of the input signatures (either numeric or symbolic) and c is the number of novelty detectors. [sent-149, score-0.94]

62 A classiﬁcation example An architecture capable of discriminating two shape classes consists of a cascade of two classiﬁcation modules. [sent-151, score-0.37]

63 The ﬁrst module identiﬁes the components of each shape class, while the second veriﬁes the geometric consistency (spatial relationships) of the components. [sent-152, score-0.512]

64 Figure 4 illustrates the classiﬁcation procedure on two sample surface meshes from a test set of 200 human heads. [sent-153, score-0.541]

65 The ﬁrst mesh (Figure 4 a) belongs to the class of healthy individuals, while the second (Figure 4 e) belongs to the class of individuals with a congenital syndrome that produces a pathological craniofacial deformation. [sent-154, score-0.713]

66 The input classiﬁcation module was trained with a set of 400 surface meshes and 4 critical points per class to recognize the eight components shown in Figure 4 b and f. [sent-155, score-0.981]

67 Each of the test surface meshes was individually processed as follows. [sent-157, score-0.502]

68 Given an input surface mesh to the ﬁrst classiﬁcation module, the classiﬁer ensemble (component detectors and components classiﬁer) is applied to the numeric surface signatures of its points (Figure 4 a and e). [sent-158, score-1.917]

69 A connected components algorithm is then applied to the result and components of size below a threshold (10 mesh points) are discarded. [sent-159, score-0.506]

70 After this process the resulting labeled mesh is fed to the second classiﬁcation module that was trained with 400 labeled meshes and two critical points to recognize two new components. [sent-160, score-1.023]

71 Consequently, the points of the output mesh of the second module will be set to “+1” if they belong to learned symbolic signatures associated with the healthy heads (Figure 4 c) , and “-1” otherwise (Figure 4 g). [sent-164, score-1.365]

72 Figure 4 c (g) shows the region found by our algorithm that corresponds to the shape class model of normal (respectively abnormal) head. [sent-166, score-0.458]

73 For classiﬁcation with human heads the data consisted of 600 surface mesh models (400 training samples and 200 testing samples). [sent-177, score-0.902]

74 For the faces, the data sets consisted of 300 surface meshes (200 training samples and 100 testing samples). [sent-179, score-0.582]

75 The corresponding mesh resolution was set to about 0. [sent-180, score-0.366]

76 All the surface models considered here were obtained from range data scanners and all the deformable models were constructed using the methods described in [10]. [sent-182, score-0.434]

77 We tested the stability in the formation of shape class components using the faces data set. [sent-183, score-0.436]

78 This set contains a signiﬁcant amount of shape variability. [sent-184, score-0.287]

79 The ﬁrst module of our classiﬁer must generate stable components to allow the second module to discriminate their corresponding geometric conﬁgurations. [sent-188, score-0.445]

80 We trained the ﬁrst classiﬁcation module with a set of 200 faces using critical points arbitrarily located on the cheek, chin, forehead and philtrum of the surface models. [sent-189, score-0.783]

81 This rate is reasonably high considering the amount of shape variability in the data set (Fig. [sent-192, score-0.287]

82 We performed classiﬁcation of normal versus abnormal human heads, a task that often occurs in medical settings. [sent-195, score-0.336]

83 The surface meshes of each of these examples were convex combinations of normal and abnormal heads. [sent-202, score-0.761]

84 Our shape classiﬁer was able to discriminate with high accuracy between normal and abnormal models. [sent-207, score-0.567]

85 It was also able to discriminate classes that share a signiﬁcant amount of common shape features ( see II-B∗ in Table 1). [sent-208, score-0.391]

86 The methods cited in the introduction were not considered for direct comparison, because they use global shape representations that were designed for classifying complete 3-D models. [sent-211, score-0.263]

87 Our approach using symbolic signatures can operate on single-view data sets containing partial model information, as shown by the experimental results performed on several shape classes [10]. [sent-212, score-0.952]

88 4 Discussion and Conclusion We presented a supervised approach to classiﬁcation of 3-D shapes represented by range data that learns class components and their geometrical relationships from surface descriptors. [sent-214, score-0.59]

89 abnormal) and studied the stability in the formation of class components using a collection of real face models containing a large amount of shape variability. [sent-216, score-0.427]

90 The numeric and symbolic shape descriptors considered here are important. [sent-220, score-0.752]

91 For example, the spin image deﬁned on the forehead (point P) in Figure 3 encodes information about the shape of most of the face (including the chin). [sent-222, score-0.422]

92 Spin images and some variants [11] are reliable for encoding surface shape in the present context. [sent-224, score-0.597]

93 Other descriptors such as curvature-based or harmonic signatures are not descriptive enough or lack robustness to scene clutter and occlusion. [sent-225, score-0.584]

94 Nevertheless, the shape descriptors cap2 Test samples were obtained from models with craniofacial features based upon either the Greig cephalopolysyndactyly (A) or the trisomy 9 mosaic (B) syndromes [6]. [sent-227, score-0.502]

95 tured enough global information to allow a classiﬁer to discriminate between the distinctive features of normal and abnormal heads. [sent-228, score-0.34]

96 The structure of the classiﬁcation module (bank of novelty detectors and multi-class classiﬁer) is important. [sent-229, score-0.332]

97 The experimental results showed us that the output of the novelty detectors is not always reliable and the multi-class classiﬁer becomes critical for constructing stable and consistent class components. [sent-230, score-0.361]

98 The essential point consists of generating groups of neighboring surface points whose shape descriptors are similar but distinctive enough from the signatures of other components. [sent-234, score-1.261]

99 1) Our method is able to model shape classes containing signiﬁcant shape variance and can absorb about 20% of scale changes. [sent-236, score-0.585]

100 However, larger sets are required in order to capture the shape variability of the abnormal craniofacial features due to race, age and gender. [sent-239, score-0.52]

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