cvpr cvpr2013 cvpr2013-321 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Yen H. Le, Uday Kurkure, Ioannis A. Kakadiaris
Abstract: Statistical shape models, such as Active Shape Models (ASMs), sufferfrom their inability to represent a large range of variations of a complex shape and to account for the large errors in detection of model points. We propose a novel method (dubbed PDM-ENLOR) that overcomes these limitations by locating each shape model point individually using an ensemble of local regression models and appearance cues from selected model points. Our method first detects a set of reference points which were selected based on their saliency during training. For each model point, an ensemble of regressors is built. From the locations of the detected reference points, each regressor infers a candidate location for that model point using local geometric constraints, encoded by a point distribution model (PDM). The final location of that point is determined as a weighted linear combination, whose coefficients are learnt from the training data, of candidates proposed from its ensemble ’s component regressors. We use different subsets of reference points as explanatory variables for the component regressors to provide varying degrees of locality for the models in each ensemble. This helps our ensemble model to capture a larger range of shape variations as compared to a single PDM. We demonstrate the advantages of our method on the challenging problem of segmenting gene expression images of mouse brain.
Reference: text
sentIndex sentText sentNum sentScore
1 edu/ Abstract Statistical shape models, such as Active Shape Models (ASMs), sufferfrom their inability to represent a large range of variations of a complex shape and to account for the large errors in detection of model points. [sent-9, score-0.456]
2 We propose a novel method (dubbed PDM-ENLOR) that overcomes these limitations by locating each shape model point individually using an ensemble of local regression models and appearance cues from selected model points. [sent-10, score-0.837]
3 Our method first detects a set of reference points which were selected based on their saliency during training. [sent-11, score-0.48]
4 From the locations of the detected reference points, each regressor infers a candidate location for that model point using local geometric constraints, encoded by a point distribution model (PDM). [sent-13, score-0.605]
5 The final location of that point is determined as a weighted linear combination, whose coefficients are learnt from the training data, of candidates proposed from its ensemble ’s component regressors. [sent-14, score-0.388]
6 We use different subsets of reference points as explanatory variables for the component regressors to provide varying degrees of locality for the models in each ensemble. [sent-15, score-0.792]
7 This helps our ensemble model to capture a larger range of shape variations as compared to a single PDM. [sent-16, score-0.423]
8 We demonstrate the advantages of our method on the challenging problem of segmenting gene expression images of mouse brain. [sent-17, score-0.755]
9 The active shape model (ASM [7]) is one of the most popular statistical shape models that restricts the shape space to limit the range of possible shapes the model can form. [sent-21, score-0.802]
10 However, one of their major limitations lies in their ability to represent the variations of a complex shape model, especially when the number of training samples is much smaller than the dimensions of the shape model. [sent-22, score-0.394]
11 Such erroneous detections of a large number of model points can drive the fitting to an incorrect solution. [sent-25, score-0.356]
12 In this paper, we propose a new approach for statistical model fitting that also provides solutions to the problems of the model flexibility and the model point detection errors. [sent-26, score-0.511]
13 Our PDM-ENLOR locates each shape model point individually using an ensemble of regression models built for that specific point. [sent-27, score-0.79]
14 Specifically, a set of salient reference points are first selected to be used as explanatory variables of the regression models. [sent-28, score-0.815]
15 These reference points are detected using our PASM-CTX algorithm. [sent-29, score-0.444]
16 Then, each component regression model regresses the location of a model point of interest from the detected locations of its explanatory variables by fitting a point distribution model (PDM) [8], which is built to encode the spatial relationship between the dependent and the explanatory variables. [sent-30, score-0.916]
17 In order to provide increased flexibility to the shape model and to handle the non-robust detection of the regression explanatory variables, the models are built with increasing degrees of locality based on the increasing number of reference points used. [sent-31, score-1.23]
18 Note that the set of selected salient reference points is automatically selected during the training phase and may include points that do not belong to the boundaries. [sent-33, score-0.752]
19 We evaluate our method on mouse brain gene expression images to segment sagittal sections from a mouse brain into 14 anatomical regions. [sent-34, score-1.495]
20 The main challenges of this problem are the lack of visible edge cues of the regional boundaries and the shape variation of anatomical regions across images [16]. [sent-35, score-0.352]
21 First, we propose a novel method to construct an ensemble of multiple regression models to impose shape constraints of varying degrees of locality from local-to-global to increase the 111888777866 flexibility of the shape model. [sent-37, score-0.978]
22 Third, our PASM-CTX method to detect the reference points is the first work that uses similaritybased features instead of a local gray level model to detect the local best matches in ASM search. [sent-41, score-0.488]
23 This modification makes ASM applicable to gene expression image data whose regional boundaries are indistinct. [sent-42, score-0.536]
24 In addition, since our method incorporates appearance guidance from only the points that are likely to be detected correctly, our method does not require any post-processing step to minimize the errors in fitting due to unreliable model points. [sent-43, score-0.544]
25 Instead of partitioning the shapes, few recent methods [2, 18] fit a global shape model for each model point individually using local weights. [sent-59, score-0.376]
26 The local weights for each model point control the neighborhood size for fitting that point and they are computed based on the distances between model points. [sent-60, score-0.453]
27 While this approach avoids the partitioning of the shape model, determining the neighborhood size that controls the degree of locality is nontrivial. [sent-61, score-0.395]
28 [29] proposed to detect the salient points based on prior knowledge about the contrast of the contour and reconstruct the full shape from the detection of salient points. [sent-70, score-0.57]
29 However, instead of using a single global model, our method explicitly builds different regression models with different degrees of locality for each point to increase their flexibility. [sent-75, score-0.426]
30 Similar to [29], the PASM-CTX and PDM-ENLOR detect the salient points and reconstructs the shape based on the guidance of the salient points to account for the large errors in detection. [sent-77, score-0.733]
31 However, our methods learn the set of salient points from training data in advance and exploits information from additional supporting salient points, which may not belong to the boundaries. [sent-78, score-0.37]
32 In addition, PDM-ENLOR uses salient points selectively in the ensemble of multiple models to provide further flexibility at local level. [sent-79, score-0.538]
33 Overview In this section, we briefly present our method for fitting a shape model to an image. [sent-85, score-0.392]
34 A set of reference points, which were selected during training phase based on a saliency criteria, are detected using PASM-CTX. [sent-87, score-0.415]
35 Then, each point of the boundary shape model is localized independently using an ensemble of regression models. [sent-88, score-0.704]
36 Each regression model is obtained by fitting a PDM, which is specifically built to represent the spatial relationship of the model point of interest and a subset of the reference points. [sent-89, score-0.774]
37 Specifically, the final location of a model point pi in the shape model of interest, is given by: = ? [sent-92, score-0.466]
38 j=1 (1) where k is the number of regression functions built for pi, Rji is a set of reference points used in the function fji to infer pi and cji is the ensemble coefficient for the regression 111888777977 function fji. [sent-95, score-1.207]
39 The shape model of interest that contains sampled points on the boundaries of the object is referred as the boundary shape model. [sent-97, score-0.597]
40 Reference point selection Only the points that can be reliably detected should be used as a reference to guide the inference for the location of the model points. [sent-102, score-0.556]
41 The similarity-saliency score of a point u with respect to a reference image T computed for a set of training images I {Ii}in=1 is defined as: = γ(u,T,I) = ? [sent-107, score-0.372]
42 First, the similarity-saliency score of each point with respect to the reference image T over the set of training images I (Eq. [sent-121, score-0.372]
43 Then, a set of reference points ewsh Ios (eE similarity-saliency score i,s higher ft rheafna threshold t are selected. [sent-123, score-0.405]
44 Mouse brain gene expression images: For mouse brain images, L contains all 1,245 vertices of a subdivision mesh, a geometric model specifically constructed for mouse brain gene expression images by Ju et al. [sent-133, score-2.178]
45 For the 10-fold experiments, 183 to 196 reference points were selected and depicted as solid blue circles in Fig. [sent-136, score-0.441]
46 In the mouse brain gene expression images, the intensity pattern of each anatomical region may vary significantly from image to image as each image expresses a different gene. [sent-138, score-1.025]
47 Therefore, a special image called Nissl-stained image (NSI), which was constructed using a universal gene probe and has maximum similarity to other gene expression images, is used as a reference image ([16, 20]). [sent-139, score-1.123]
48 Regression model definition In this section, we present how to encode different degrees of locality in our ensemble scheme by defining the explanatory variables Rji for regressors in Eq. [sent-142, score-0.598]
49 The locality level j of a regression model fji (Rij) is based on the spatial relationship between pi and the reference points in Rji . [sent-144, score-0.954]
50 We assume that the neighboring points provide simi- Figure 1: Illustration of the shape models in mouse brain gene expression image segmentation. [sent-145, score-1.263]
51 The squares depict the non-reference boundary points and the solid blue circles depict the reference points. [sent-146, score-0.463]
52 The boundary shape model contains all sampled points on the regional boundaries of 14 anatomical regions. [sent-147, score-0.593]
53 The extended shape model contains all the boundary points and the reference points (i. [sent-148, score-0.855]
54 These clusters of the reference points are then used to construct the regression models for inference of the position of a target model point. [sent-156, score-0.676]
55 Because there can be some reference points that are isolated from the others and should not be merged with their neighbors that are far away, we allow the clusters to have size of 1. [sent-168, score-0.489]
56 The smk−a1lle∪r vQalue of, tfoher locality le (kve −l j o)f; the regression −m1odel fji corresponds to a more local model. [sent-186, score-0.412]
57 Shape model point regression Given an input image, our method first detects the reference points and then infers the position of each model point using the constructed regression models. [sent-190, score-0.974]
58 For clarity of presentation, first we present how to determine candidate locations using a PDM-based regression function assuming that the positions of the reference points are already available. [sent-191, score-0.557]
59 1 PDM-based model point regression In this section, we present how our method infers the po- sition of a model point pi based on reference points in Rji using a PDM. [sent-195, score-0.957]
60 Then, each shape x is represented as x = ¯x Pb, where b is the shape parameter. [sent-202, score-0.356]
61 The fitting of the PDM ( x¯, P) to a shape x is given by: + x∗ = argminx | |W[x − ( x¯ + Pb)] | |22 , (5) where the diagonal weight matrix W2m×2m is introduced to emphasize the importance of the model points: W(2i − 1, 2i − 1) = W(2i, 2i) is the weight of the ith Wmod(2eil point. [sent-203, score-0.392]
62 Generally, the shape is rigidlyaligned before fitting to remove global transformations by using generalized Procrustes [14]. [sent-205, score-0.351]
63 ,ekre −ea 1ch), shape Mco (n x¯tains pi (always being the first point of the shape) and all points in Rji . [sent-212, score-0.526]
64 To use a PDM to infer the position of an unknown point pi, we reconstruct the full shape from the known locations of points in Rji and retrieve the point of interest pi. [sent-213, score-0.462]
65 The inference of pi in the first (k −1) regression models employs only the geometric c foirnsstt (raki−nts1 b)e rtewgreeesns pi amnodd tehles reference points. [sent-216, score-0.757]
66 To explicitly impose the geometric constraints on all the points in the boundary shape model, the extended shape model is used for training the PDM for the last regressor fki (Rik). [sent-217, score-0.704]
67 In the ASM approach, a shape iteratively evolves in two steps: (i) finding a new shape estimate (target shape) whose each model point is detected as the best match in the local neighborhood of that point from the previous iteration, and (ii) fitting the target shape by solving Eq. [sent-221, score-0.985]
68 Due to the indistinct anatomical boundaries in gene expression images, the local gray level model of the traditional ASM formulation is not suitable for the detection of the model points. [sent-223, score-0.704]
69 While we want to detect only the reference points, the extended shape model is used to train a PDM for maintaining the global shape constraint. [sent-225, score-0.691]
70 Since the extended shape model contains context points which are not the points of interest, we refer our modified ASM method as PASM-CTX (Partial ASM with ConTeXt). [sent-226, score-0.534]
71 At each iteration, we evolve the shape based on the guidance of the reference points only (i. [sent-227, score-0.633]
72 , 0 as weight for non-reference points and 1 as weight for reference points in the fitting process). [sent-229, score-0.72]
73 That means the fitting step at the last iteration is omitted and the best matches obtained from feature detectors at that iteration are the final estimates of the reference points. [sent-231, score-0.492]
74 Initialization: To obtain a robust initialization for the specific application, the shape parameters are first computed based on the points on the outer boundary of the brain (i. [sent-232, score-0.565]
75 The reason is that the outer boundary in mouse brain can be easily obtained quite accurately and it can provide certain information about the global shape [15, 4, 17, 20]. [sent-235, score-0.7]
76 The neighboring point whose image patch around it in the test image is most similar to the image patch around pi in the reference image (NSI) is selected as the best match for pi. [sent-243, score-0.505]
77 Combining the models in ensemble In this section, we provide the motivation for using an ensemble of models in Eq. [sent-252, score-0.476]
78 Using an ensemble of models: A local model can pro- vide improved geometric constraints due to the locality and the simplicity of the local shape. [sent-255, score-0.412]
79 Using a global model in this case can help if the additional reference points can be detected more accurately. [sent-257, score-0.485]
80 Learning the ensemble weights: For each model point pi, the coefficient vector ci = [ci1, ci2, . [sent-269, score-0.35]
81 The matrix Ai contains the coordinates of the results obtained from the regression models that infer pi in all training images: Il. [sent-273, score-0.359]
82 Then, the ensemble coefficient vector for point pi is computed as: (xi(g,l) y(ig,l) ci∗= argcmiin||Aici− gi||22, s. [sent-280, score-0.444]
83 Experiments and Results Image data: We evaluated our method on 2D mouse brain gene expression images [4, 6]. [sent-285, score-0.909]
84 The dataset contains 100 images depicting sagittal sections of postnatal day 7 mouse brains at standard section 9. [sent-286, score-0.364]
85 The annotated shape and the anatomical point set L were extracted from the manually annotated subdivision mesh at subdivision level 2 and were provided by [15, 4]. [sent-288, score-0.659]
86 We quantitatively compared the performance of the different methods using the Dice similarity coefficient (DSC) against the manual annotations for each of the 14 anatomical regions in the mouse brain. [sent-290, score-0.458]
87 That can be explained by the non-robust detections of large number of model points due to the complex appearance of gene expression images. [sent-330, score-0.696]
88 Comparison with previous works on the application: We also compared our method PDM-ENLOR with two state-of-the-art works on mouse brain gene expression image data of Kurkure et al. [sent-340, score-0.909]
89 Conclusions In this paper, we have presented a new approach to improve the model flexibility and to handle the detection errors for statistical shape fitting problem towards image segmentation. [sent-346, score-0.567]
90 We proposed to locate each model point individually using an ensemble of PDM-based regression models which were constructed with increasing degree of locality to provide more flexibility. [sent-347, score-0.708]
91 A set of selected salient reference points is used to construct the models to minimize the errors in fitting due to unreliable model points. [sent-353, score-0.848]
92 We demonstrated that the use of appearance cues from selected model points can significantly improve the fitting results. [sent-355, score-0.427]
93 Furthermore, our method outperforms the state-of-the-art methods on a challenging problem of multiregion segmentation ofthe mouse brain gene expression images. [sent-356, score-0.909]
94 Learning-based segmentation framework for tis111888888422 [5] [6] [7] [8] sue images containing gene expression data. [sent-394, score-0.478]
95 Automated pipeline for atlas-based annotation of gene expression patterns: Application to postnatal day 7 mouse brain. [sent-423, score-0.803]
96 Adapting active shape models for 3D segmentation of tubular structures in medical images. [sent-461, score-0.366]
97 Similarity-based appearance prior for fitting a subdivision mesh in gene expression images. [sent-546, score-0.853]
98 Discrete deformable model guided by partial active shape model for trus image segmentation. [sent-619, score-0.354]
99 Towards robust and effective shape modeling: sparse shape composition. [sent-633, score-0.356]
100 A novel 3d partitioned active shape model for segmentation of brain mr images. [sent-641, score-0.439]
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