## Discriminative learning of Markov random fields for segmentation of 3d scan data (2005)

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Venue: | In Proc. of the Conf. on Computer Vision and Pattern Recognition (CVPR |

Citations: | 107 - 5 self |

### BibTeX

@INPROCEEDINGS{Anguelov05discriminativelearning,

author = {Dragomir Anguelov and Ben Taskar and Vassil Chatalbashev and Daphne Koller and Dinkar Gupta and Geremy Heitz and Andrew Ng},

title = {Discriminative learning of Markov random fields for segmentation of 3d scan data},

booktitle = {In Proc. of the Conf. on Computer Vision and Pattern Recognition (CVPR},

year = {2005},

pages = {169--176}

}

### Years of Citing Articles

### OpenURL

### Abstract

We address the problem of segmenting 3D scan data into objects or object classes. Our segmentation framework is based on a subclass of Markov Random Fields (MRFs) which support efficient graph-cut inference. The MRF models incorporate a large set of diverse features and enforce the preference that adjacent scan points have the same classification label. We use a recently proposed maximummargin framework to discriminatively train the model from a set of labeled scans; as a result we automatically learn the relative importance of the features for the segmentation task. Performing graph-cut inference in the trained MRF can then be used to segment new scenes very efficiently. We test our approach on three large-scale datasets produced by different kinds of 3D sensors, showing its applicability to both outdoor and indoor environments containing diverse objects. 1.

### Citations

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Citation Context ...assume a pre-specified generative model. Our segmentation approach is most closely related to work in vision applying conditional random fields (CRFs) to 2D images. Discriminative models such as CRFs =-=[15]-=- are a natural way to model correlations between classification labels Y given a scan X as input. CRFs directly model the conditional distribution P (Y | X). In classification tasks, CRFs have been sh... |

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Citation Context ...min-cut algorithm. In the case of binary labels (K = 2), the min-cut procedure is guaranteed to return the optimal MAP. For K > 2, the MAP problem is NPhard, but a procedure proposed by Boykov et al. =-=[1]-=-, which augments the min-cut algorithm with an iterative procedure called alpha-expansion, guarantees a factor 2 approximation of the optimal solution. An alternative approach to solving the MAP infer... |

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Citation Context ...ta which is often noisy and sparse. The 3D scan segmentation problem has been addressed primarily in the context of detect1 ing known rigid objects for which reliable features can be extracted (e.g., =-=[11, 5]-=-). The more difficult task of segmenting out object classes or deformable objects from 3D scans requires the ability to handle previously unseen object instances or configurations. This is still an op... |

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Citation Context ...etwork is to find arg maxy Pφ(y). We further restrict our attention to an important subclass of networks, called associative Markov networks (AMNs) [21] that allow effective inference using graphcuts =-=[8, 13]-=-. These associative potentials generalize the Potts model [16], rewarding instantiations where adjacent nodes have the same label. Specifically, we require that φij(k, k) = λk ij , where λkij ≥ 1, and... |

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Citation Context ... to handle previously unseen object instances or configurations. This is still an open problem in computer vision, where many approaches assume that the scans have been already segmented into objects =-=[10, 6]-=-. An object segmentation algorithm should possess several important properties. First, it should be able to take advantage of several qualitatively different kinds of features. For example, trees may ... |

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Citation Context ...een demonstrated [18]. Another line of work performs classification of 3D 2 shapes. Some methods (particularly those used for retrieval of 3D models from large databases) use global shape descriptors =-=[6, 17]-=-, which require that a complete surface model of the query object is available. Objects can also be classified by looking at salient parts of the object surface [10, 19]. All mentioned approaches assu... |

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Citation Context ...imation of the optimal solution. An alternative approach to solving the MAP inference problem is based on formulating the problem as an integer program, and then using a linear programming relaxation =-=[2, 12]-=-. This approach is slower in practice than the iterated min-cut approach, but has the same performance guarantees [21]. Importantly for our purposes, it forms thesbasis for our learning procedure. We ... |

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Citation Context ...efficient, scaling to scenes involving millions of points. It produces the optimal solution for binary classification problems and a solution within a fraction of the optimal for multi-class problems =-=[12]-=-. We demonstrate the approach on two real-world datasets and one computer-simulated dataset. These data sets span both indoor and outdoor scenes, and a diverse set of object classes. They were acquire... |

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Citation Context ... well as formal guarantees for binary classification problems. Unlike their work, our approach can also handle multi-class problems in a straightforward manner. In a very recent work, Torralba et al. =-=[23]-=- propose boosting random fields for image segmentation, combining ideas from boosting and CRFs. Similar to our approach, they optimize the classification margin. However, their implementation is speci... |

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Citation Context ...on to an important subclass of networks, called associative Markov networks (AMNs) [21] that allow effective inference using graphcuts [8, 13]. These associative potentials generalize the Potts model =-=[16]-=-, rewarding instantiations where adjacent nodes have the same label. Specifically, we require that φij(k, k) = λk ij , where λkij ≥ 1, and φij(k, l) = 1, ∀k �= l. We formulate the node and edge potent... |

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Citation Context ...ta which is often noisy and sparse. The 3D scan segmentation problem has been addressed primarily in the context of detect1 ing known rigid objects for which reliable features can be extracted (e.g., =-=[11, 5]-=-). The more difficult task of segmenting out object classes or deformable objects from 3D scans requires the ability to handle previously unseen object instances or configurations. This is still an op... |

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Citation Context ...or to generative approaches which expend efforts to model the potentially more complicated joint distribution P (X, Y) [15]. Very recently, CRFs have been applied for image segmentation. Kumar et al. =-=[14]-=- train CRFs using a pseudo-likelihood approximation to the distribution P (Y | X) since estimating the true conditional distribution is intractable. Unlike their work, we optimize a different objectiv... |

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Citation Context ... also tested our scan segmentation algorithm on a challenging dataset of cluttered scenes containing articulated wooden puppets. The dataset was acquired by a scanning system based on temporal stereo =-=[4]-=-. The system consists of two cameras and a projector, and outputs a triangulated surface only in the areas that are visible to all three devices simultaneously. The dataset contains eleven different s... |

73 | Learning associative Markov networks
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Citation Context ...ghts. We use a maximum-margin learning approach which finds the optimal tradeoff between the node and edge features, which induce the MRF-based segmentation algorithm to match the training set labels =-=[21]-=-. This learning procedure finds the globally optimal (or nearly optimal) weights and can be implemented efficiently. In the segmentation phase, we need to classify the points of a new scene. We comput... |

70 | Shape contexts enable efficient retrieval of similar shapes
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Citation Context ...e classified into three groups. The first class of methods detects known objects in the scene. Such approaches center on computing efficient descriptors of the object shape at selected surface points =-=[11, 7, 5]-=-. However, they usually require that the descriptor parameters are specified by hand. Detection often involves inefficient nearest-neighbor search in highdimensional space. While most approaches addre... |

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30 | Parts-based 3d object classification
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Citation Context ... to handle previously unseen object instances or configurations. This is still an open problem in computer vision, where many approaches assume that the scans have been already segmented into objects =-=[10, 6]-=-. An object segmentation algorithm should possess several important properties. First, it should be able to take advantage of several qualitatively different kinds of features. For example, trees may ... |

27 | A new paradigm for recognizing 3d object shapes from range data
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Citation Context ...tection often involves inefficient nearest-neighbor search in highdimensional space. While most approaches address detection of rigid objects, detection of nonrigid objects has also been demonstrated =-=[18]-=-. Another line of work performs classification of 3D 2 shapes. Some methods (particularly those used for retrieval of 3D models from large databases) use global shape descriptors [6, 17], which requir... |

21 |
T.: The princeton shape benchmark. In: Shape Modeling International
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Citation Context ... set of artificially generated scenes, which contain different types of vehicles, trees, houses, and the ground. Models of the objects in these scenes were obtained from the Princeton Shape Benchmark =-=[20]-=-, and were combined in various ways to construct the training and test scenes. From these, a set of synthetic range scans were generated by placing a virtual sensor inside the scene. We corrupted the... |

5 |
What energy functions can be minimized using graph cuts
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Citation Context ...contiguity of the labels; the strength of these links can also depend on features (e.g., distance between the linked points). We use a subclass of MRFs that allow effective inference using graph cuts =-=[13]-=-, yet can enforce our spatial contiguity preference. Our algorithm consists of a learning phase and a segmentation phase. In the learning phase, we are provided a set of scenes acquired by a 3D scanne... |

5 | Discriminating deformable shape classes
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Citation Context ...s) use global shape descriptors [6, 17], which require that a complete surface model of the query object is available. Objects can also be classified by looking at salient parts of the object surface =-=[10, 19]-=-. All mentioned approaches assume that the surface has already been pre-segmented from the scene. Another set of approaches segment 3D scans into a set of predefined parametric shapes. Han et al. [9] ... |

4 |
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Citation Context ... 19]. All mentioned approaches assume that the surface has already been pre-segmented from the scene. Another set of approaches segment 3D scans into a set of predefined parametric shapes. Han et al. =-=[9]-=- present a method based for segmenting 3D images into 5 parametric models such as planar, conic and B-spline surfaces. Unlike their approach, ours is aimed at learning to segment the data directly int... |