【摘要】：形状分析是计算机视觉领域的经典问题,目前已有大量关于形状分类问题的研究.但是,当处理大的非线性失真、特别是结构上或者关联上的失真时,许多形状分类方法往往无能为力.提出一种利用轮廓关键点集(contour critical point sets,CCPS)进行形状分类的新方法.轮廓关键点的特征用其inner-distance形状上下文(IDSC)表征.关键点的inner-distance形状上下文不仅表征形状的局部特征,也反映其全局特征,这种局部点的全局特征信息对遮挡、非线性失真等有良好的鲁棒性.巧妙地构造关键点的特征向量后,对形状轮廓关键点集、形状类、和全体形状样本建模,进行三级的贝叶斯分类.形状类模型使得可以利用同一类中的不同样本的不同关键点对输入形状进行识别.实验结果表明,这种基于视觉部分的全局特征,三级的贝叶斯分类方法对非线性失真、类内变异、结构变化、遮挡等具有良好的鲁棒性.文中的方法在Kimia形状数据库上达到100%的分类精度,并且分类所有108个测试形状仅需要8s,是目前已知最好的分类性能.在广泛使用的MPEG-7形状数据库上,也能达到满意的分类结果.
Abstract: Shape analysis has been one of the most studied topics in computer vision. One major task in shape analysis is to study the underlying statistics of shape population and use the information to extract , recognize , and understand physical structures and biological objects. Matching based algorithms perform classification , essentially through exemplar based or nearest neighborhood approach by matching the query shape against all those in the training set. On few training samples , these algorithms are hard to capture the large intra-class variation. On large training samples , it is extremely time consuming to perform shape matching one-by-one. Approaches based on generative models require a large number of parameters , which renders them significantly more expensive computationally , and also increases the possibility of converging to non-optimal local minima. Furthermore , existing Matching based and model-based approaches cannot handle object classes that have different parts or numbers of parts without splitting the class into separate subclasses. Most of the methods for shape classification are based on contour and many researchers have worked on the general shape classification problem. However , approaches for classifying contour shapes can encounter difficulties when dealing with classes that have large nonlinear variability , especially when the variability is structural or due to articulation. A novel method , using Contour Critical Point Sets (CCPS) to perform shape classification task , is proposed in this paper. First , Inner-Distance Shape Context (IDSC) is used to characterize the critical points. Of course , other features of the critical points may instead of IDSC. Shapes are represented by a set of points sampled from the shape contours and the shape context at a reference point captures the distribution of the remaining points relative to it , thus offering a globally discriminative characterization. Corresponding points on two similar shapes will have similar shape contexts. The inner-distance is defined as the length of the shortest path between landmark points within the shape silhouette. It is articulation insensitive and more effective at capturing part structures than the Euclidean distance. This suggests that the inner-distance can be used as a replacement for the Euclidean distance to build more accurate descriptors for complex shapes , especially for those with articulated parts. Humans perception of shape is based on similarity of common parts , to the extent that a single, significant visual part is sufficient to recognize the whole object and part-based representations allow for recognition that is robust in the presence of occlusion, movement, deletion, or growth of portions of an object. It is a simple and natural observation that maximal convex or concave parts of objects determine visual parts. So the contour critical point sets (CCPS) of shapes is utilized to perform shape classification task. The IDSC of critical point is an excellent feature of contour point, which not only contains local features but also the global information. After design the smart feature of shapes , then , Bayesian classification is performed within a three-level framework which consists of models for contour critical point sets , for classes , and for the entire database of training examples. The class model enables different critical points of different exemplars of one class to contribute to the recognition of an input shape. This new method achieves 100% classification accuracy on Kimia database. Furthermore , to classify all 108 test shapes only need 8 seconds , which is the best performance ever reported in the literature. The results on the well-known MPEG7 CE-Shape-1 data set also prove its superiority.
Fig.2 Inner-Distance Shape Context of critical points 图 2 轮廓关键点的Inner-Distance形状上下文
Fig.3 All test shapes’ posterior probability result 图 3 后验概率,横轴为类别标号,纵轴为形状标号
Kimia 数据库上实验结果，分类精度100%
Fig.4 Classification accuracy versus occlusion 图 4 对遮挡和特征缺失的分类精度
对特征缺失有很好的鲁棒性，因此对遮挡等有效。
Table 1 Comparison on Kimia dataset
表1 Kimia形状数据库上分类性能比较
Method
Accuracy (%)
Time (s)
Critical Points
100 (108 training)
0.07
Sun & Super[3]
97.2(leave-one out)
12.5
Skeleton Path[19]
94.4(leave-one out)
7
Table 2 Classification results of Different Methods for the MPEG7 CE-Shape-1
表2 MPEG-7形状数据库上各方法分类性能比较
Method
700 training accuracy (%)
Leave one out accuracy (%)
Features (万)
Time (s)
CCPS
88.714
92.429
1.8
0.5
Sun & Super[3]
93
97.9
12
7
Shape Context[1]
------
94
14
≈100
与文中结果相比较的文献：
[1] S. Belongie, J. Malik, and J. Puzicha. Shape matching and object recognition using shape contexts. IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 2002, 24(4): 509~522. [3] Sun, K, Super, B. Classification of contour shapes using class segment sets. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2005,CVPR 2005, IEEE Computer Society Conference on. Vol. 2, 727~733. [19] Xing-Wei Yang, Xiang Bai, and Longin Jan Latecki. Shape Classification Based on Skeleton Path Similarity. 6th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR), EZhou, China, August, 2007.
