Cao Mengfei

Semantic Analysis Recognition Spectrum- based spectrum corresponden ce linprog-basedclustering Ⅰ. Warm-ups: Ⅱ. abstract Ⅲ. a special example and its counterpart Ⅳ. extension

Recognition: based on feature but what if what you get is not what you really want? Semantic Analysis: various methods; however it will be great when something happens like this: “Hierarchical Semantics of Objects ” ----ICCV2005

Related saying: " 一般的点模式匹配问题是模式识别中的一个有名的难 题, 人们对一般的点模式匹配问题提出过很多的算法, 像 Sanjay Ranade 等人的松弛算法、 Shih-hsu Chang 等人的 基于二维聚类的快速算法、 Zsolt Miklós 等人的三角匹 配的算法、 Xudong Jiang 等人 [9] 的基于局部和全局结构 的匹配算法." 摘抄自 自动指纹识别中的图像增强 和细节匹配算法 My feeling: search for the pairwise through similarities of objective- data

according to the ways of making use of the similarites: Direct Comparison Distance of feature, similarity of inter_data instead of intra_data eg. enumerate Consistency Constraints Groupwise of Pairwise based on distance Groupwise of Pairwise based on more sophisticated geometric properties

Compare the Similarity: (i-i’),(i-j’),(j-i’),(j-j’) Compare Consistency: (i-j) v.s. (i’-j’) Ⅰ.Ⅰ. Ⅱ.Ⅱ. calculation accuracy

（ 1 ） to find out the outliers in the first set; （ 2 ） to find out the outliers in the second set; robust to the outliers （ 3 ） to find out all the correct correspondent pairwises. robust to the noise Affine transformation, translation, scalar transformation illumination, rotation, diversity``````

Spectrum of Matrix: Magical Mathematical Object- properties, instead of pure Consciousness. objective, descriptive, essential Based on eigen values & eigen vectors. Related saying: music is dynamic, while score is static; movement is dynamic, while law is static GraphAdjacency MatrixSpectrum Model the reality

Calculation, Accuracy imagematrixgraph

Basic problem in the field of pattern recognition Various methods used in various situations after all, to cluster is to aggregate the objects with similar properties how to combine it to the former issues?

Marius Leordeanu and Martial Hebert International Conference of Computer Vision (ICCV), October, 2005 PhD Student, RI Vision and Autonomous Systems Center (VASC) The Robotics Institute Professor Efficient techniques for object/category recognition Use of contextual information, in particular 3-D geometry from images, for scene analysis Detection, tracking, and prediction in dynamic environments

Based on spectral theory, build the wanted matrix(similarity) Spectral Clustering Get the Correspondence

Compare the Similarity: (i-i’),(i-j’),(j-i’),(j-j’) Compare Consistency: (i-j) v.s. (i’-j’) Ⅰ.Ⅰ. Ⅱ.Ⅱ. calculation accuracy

Based on spectral theory, build the wanted matrix(similarity) Spectral Clustering Get the Correspondence

first find the principal eigenvector of M (if)Has a main strongly connected cluster formed by the correct assignments that tend to establish agreement links keep rejecting the assignments of low association incorrect assignments outside of the cluster or weakly connected to it, which do not form strongly connected clusters due to their small probability of establishing agreement links and random, unstructured way in which they form these links. the graph associated with matrix M main clusters

Matrix H represents the cost matrix of the individual correspondence (the factor ), vector x represent the corresponding indicatory correspondence. Anyway, x’*H*x stands for the correspondence-cost; thus the thing is that, as for the value, the smaller, the better, which comes to the problem of Integer Quadratic Programming--NP-complete… thus linear I.P. University of California, Berkeley CVPR

geometric distortion between pairs of corresponding feature points edge feature how similar feature points are to their corresponding feature points how much the spatial arrangement of the feature points is changed. occlusion and clutter Ⅰ. What’s special? Compared to the former

Ⅱ. Emulation: 1. deformations using white noise Ratio of time ≈ 4 : 1

2. considering the scalar and translation theoretically ， translation invariant is necessary As for the scalar transformation: Spectral:

Left: spectral right: linprog

Upper: spectral down: linprog

3. robust to the outliers 15-data, 1-15 outliers each 30 times sampling σ=2 Red: linprog method, 4235s Blue: spectral method, 13650s

“our method is orders of magnitude faster then linprog: over 400 times faster on 20 points problem sets (average time of 0.03 sec. vs 13 sec) and over 650 faster on 30 points problem sets (0.25 sec. vs 165 sec.), on a 2.4 GHz Pentium computer”

Ⅲ. Practice: Spectral Clustering Based

Linprog-based recognition:

Recognizing objects from low resolution images: Providing the semantic layout of the scene, learnt hSOs can have several useful applications such as compact scene representation for scene category classification and providing context for enhanced object detection: Ⅰ.Ⅰ. Ⅱ.Ⅱ.

Combined with direction: Affine transform What tools to use, how to use(spectral clustering) Single parameter properties Represent the relationship among data Ⅲ.Ⅲ. Ⅳ.Ⅳ.