自监督深度残差函数映射网络的3维模型对应关系计算

目的 针对传统非刚性3维模型的对应关系计算方法需要模型间真实对应关系监督的缺点,提出一种自监督深度残差函数映射网络（self-supervised deep residual functional maps network,SSDRFMN）。方法 首先将局部坐标系与直方图结合以计算3维模型的特征描述符,即方向直方图签名（signature of histograms of orientations,SHOT）描述符;其次将源模型与目标模型的SHOT描述符输入SSDRFMN,利用深度函数映射（deep functional maps,DFM）层计算两个模型间的函数映射矩阵,并通过模糊对应层将函数映射关系转换为点到点的对应关系;最后利用自监督损失函数计算模型间的测地距离误差,对计算出的对应关系进行评估。结果 实验结果表明,在MPI-FAUST数据集上,本文算法相比于有监督的深度函数映射（supervised deep functional maps,SDFM）算法,人体模型对应关系的测地误差减小了1.45;相比于频谱上采样（spectral upsampling,SU）算法减小了1.67。在TOSCA数据集上,本文算法相比于SDFM算法,狗、猫和狼等模型的对应关系的测地误差分别减小了3.13、0.98和1.89;相比于SU算法分别减小了2.81、2.22和1.11,并有效克服了已有深度函数映射方法需要模型间的真实对应关系来监督的缺点,使得该方法可以适用于不同的数据集,可扩展性大幅增强。结论 本文通过自监督深度残差函数映射网络训练模型的方向直方图签名描述符,提升了模型对应关系的准确率。本文方法可以适应于不同的数据集,相比传统方法,普适性较好。     

Coarse‐to‐Fine Isometric Shape Correspondence by Tracking Symmetric Flips

We address the symmetric flip problem that is inherent to multi‐resolution isometric shape matching algorithms. To this effect, we extend our previous work which handles the dense isometric correspondence problem in the original 3D Euclidean space via coarse‐to‐fine combinatorial matching. The key idea is based on keeping track of all optimal solutions, which may be more than one due to symmetry especially at coarse levels, throughout denser levels of the shape matching process. We compare the resulting dense correspondence algorithm with state‐of‐the‐art techniques over several 3D shape benchmark datasets. The experiments show that our method, which is fast and scalable, is performance‐wise better than or on a par with the best performant algorithms existing in the literature for isometric (or nearly isometric) shape correspondence. Our key idea of tracking symmetric flips can be considered as a meta‐approach that can be applied to other multi‐resolution shape matching algorithms, as we also demonstrate by experiments.     

字典重建和空间分布关系约束下的特征选择与图像拼接

目的 针对大型图像检索领域中,复杂图像中SIFT特征描述子的冗余和高维问题,提出了一种基于字典重建和空间分布关系约束的特征选择的方法,来消除冗余特征并保留最具表现力的、保留原始空间结构性的SIFT特征描述子。方法 首先,实验发现了特征选择和字典学习方法在稀疏表示方面的内在联系,将特征选择问题转化为字典重构任务;其次,在SIFT特征选择问题中,为了保证特征空间中特征的鲁棒性,设计了新型的字典学习模型,并采用模拟退火算法进行迭代求解;最后,在字典学习的过程中,加入熵理论来约束特征的空间分布,使学习到的特征描述子能最大限度保持原始SIFT特征空间的空间拓扑关系。结果 在公开数据集Holiday大型场景图片检索数据库上,通过与国际公认的特征选择方法进行实验对比,本文提出的特征选择方法在节省内存空间和提高时间效率（30%~ 50%）的同时,还能保证所筛选的特征描述子的检索准确率比同类特征提高8%~ 14.1%;在国际通用的大型场景图片拼接数据库IPM上,验证本文方法在图像拼接应用中特征提取和特征匹配上的有效性,实验表明本文方法能节省（50% ~70%）图像拼接时间。结论 与已有的方法比较,本文的特征选择方法既不依赖训练数据集,也不丢失重要的空间结构和纹理信息,在大型图像检索、图像拼接领域和3D检索领域中,能够精简特征,提高特征匹配效率和准确率。     

Shape matching and modeling using skeletal context

Shape is a significant visual clue for human perception and shape models show considerable promise as a basis for extracting objects from images. This paper proposes a novel approach for shape matching and modeling using the symmetry characterization of shape interior and the spatial relationships of shape structures. Based on the representative skeletal features, we develop a mechanism to generate a coarse segment matching between different instances of an object. Additionally, the natural correspondence of skeletal branches to sequential segments along the shape curves is employed in the matching process to avoid false correspondences across different segments. Point matches within the corresponding segments are then obtained by solving a constrained assignment problem. The validation of the proposed approach is illustrated on various data sets in the presence of considerable deformation and occlusion and the results are compared with those of popular approaches. We also demonstrate the performance of our method on biological objects for shape modeling, showing better models than those obtained by the state-of-the-art shape modeling approaches.     

3D Shape Matching and Inspection Using Geometric Features and Relational Learning

In this paper we consider the problem of matching 3D sensed data with models and inspection for defects where the correspondence between models and data needs to be solved in robust and efficient ways. We explore the use of machine learning (in particular, relational learning) as an efficient method for solving correspondence (and so, pose estimation) as well as automatically generating rules for acceptable shape variations from training data. As an additional but necessary issue, we also consider the use of view-independent covariance methods for the extraction of surface features used to determine shape signatures which correspond to curvature-like surface attributes. Such features are utilized in the relational learning model.     

融合特征描述符约束的3维等距模型对应关系计算

目的 为了更准确地构建3维等距模型之间的对应关系,本文提出了一种基于热核签名与波核签名的融合特征描述符计算3维等距模型对应关系的方法。方法 首先计算3维模型Laplace算子获得模型的特征向量和特征值;然后将所得到特征值和特征向量作为基参数分别计算源模型与目标模型的热核签名和波核签名,并将热核签名与波核签名融合为一个新的特征描述符。融合特征描述符作为模型上随机均匀采样点的约束,通过最小值匹配算法得到源模型和目标模型之间的对应关系。结果 实验结果表明,利用融合特征描述符约束进行计算得到的对应关系正确匹配率比热核签名约束计算得到的对应关系匹配率平均提高19.429%,比波核签名约束计算得到的对应关系匹配率平均提高4.857%。结论 本文提出的融合特征描述符适用于计算3维等距模型或近似等距的3维模型之间的对应关系,与单一使用热核签名或波核签名特征描述符相比,可以得到更加准确的对应关系。     

结合轮廓与形状特征的仿射形状匹配

目的 针对仿射变换下形状匹配中存在的描述子对形状的描述能力不足,以及描述子计算耗时大的问题,改进基于所有图像点投影的方法,提出一种利用轮廓计算投影面积的仿射形状匹配算法。方法 该算法分为粗匹配和精匹配两个阶段。粗匹配阶段以CSS角点作为备选特征点,首先统计轮廓投影面积分布作为特征点描述子;然后利用动态规划蚁群算法匹配两幅图片公共特征点序列,并将匹配好的特征点序列记为对应的新特征点;最后采用该新特征点划分目标曲线,得到对应的轮廓曲线;这一阶段的目的是对形状的筛选以及寻找一致的轮廓特征点,同时完成轮廓曲线的划分。精匹配阶段,采用小波仿射不变描述子,对粗匹配阶段匹配代价最小的5%的目标进行对应曲线匹配,得到精匹配阶段的匹配代价,从而实现对仿射目标的识别;精匹配弥补了描述子对轮廓细节描述不足的问题。结果 算法的平均检索速度比传统基于形状投影分布描述子提高44.3%,在MPEG-7图像库上的检索效果为98.65%,在MPEG-7仿射图像库上的查准率与查全率综合评价指标比传统的基于形状投影分布描述子高3.1%,比形状上下文高25%。结论 本文算法匹配效果好,效率高,抗噪性强,解决了仿射描述子计算速度慢、描述能力不足的问题,能有效地应用于仿射形状匹配与检索领域。     

Feature-Based Sequence-to-Sequence Matching

This paper studies the problem of matching two unsynchronized video sequences of the same dynamic scene, recorded by different stationary uncalibrated video cameras. The matching is done both in time and in space, where the spatial matching can be modeled by a homography (for 2D scenarios) or by a fundamental matrix (for 3D scenarios). Our approach is based on matching space-time trajectories of moving objects, in contrast to matching interest points (e.g., corners), as done in regular feature-based image-to-image matching techniques. The sequences are matched in space and time by enforcing consistent matching of all points along corresponding space-time trajectories. By exploiting the dynamic properties of these space-time trajectories, we obtain sub-frame temporal correspondence (synchronization) between the two video sequences. Furthermore, using trajectories rather than feature-points significantly reduces the combinatorial complexity of the spatial point-matching problem when the search space is large. This benefit allows for matching information across sensors in situations which are extremely difficult when only image-to-image matching is used, including: (a) matching under large scale (zoom) differences, (b) very wide base-line matching, and (c) matching across different sensing modalities (e.g., IR and visible-light cameras). We show examples of recovering homographies and fundamental matrices under such conditions.     

Scale Normalization for Isometric Shape Matching

We address the scale problem inherent to isometric shape correspondence in a combinatorial matching framework. We consider a particular setting of the general correspondence problem where one of the two shapes to be matched is an isometric (or nearly isometric) part of the other up to an arbitrary scale. We resolve the scale ambiguity by finding a coarse matching between shape extremities based on a novel scale‐invariant isometric distortion measure. The proposed algorithm also supports (partial) dense matching, that alleviates the symmetric flip problem due to initial coarse sampling. We test the performance of our matching algorithm on several shape datasets in comparison to state of the art. Our method proves useful, not only for partial matching, but also for complete matching of semantically similar hybrid shape pairs whose maximum geodesic distances may not be compatible, a case that would fail most of the conventional isometric shape matchers.     

Deblurring and Denoising of Maps between Shapes

Shape correspondence is an important and challenging problem in geometry processing. Generalized map representations, such as functional maps, have been recently suggested as an approach for handling difficult mapping problems, such as partial matching and matching shapes with high genus, within a generic framework. While this idea was shown to be useful in various scenarios, such maps only provide low frequency information on the correspondence. In many applications, such as texture transfer and shape interpolation, a high quality pointwise map that can transport high frequency data between the shapes is required. We name this problem map deblurring and propose a robust method, based on a smoothness assumption, for its solution. Our approach is suitable for non‐isometric shapes, is robust to mesh tessellation and accurately recovers vertex‐to‐point, or precise, maps. Using the same framework we can also handle map denoising, namely improvement of given pointwise maps from various sources. We demonstrate that our approach outperforms the state‐of‐the‐art for both deblurring and denoising of maps on benchmarks of non‐isometric shapes, and show an application to high quality intrinsic symmetry computation.