标签：style blog http ar io color os sp for
Bag-of-words模型是信息检索领域常用的文档表示方法。在信息检索中，BOW模型假定对于一个文档，忽略它的单词顺序和语法、句法等要素，将其仅仅看作是若干个词汇的集合，文档中每个单词的出现都是独立的，不依赖于其它单词是否出现。例如有如下两个文档：
1：Bob likes to play basketball, Jim likes too. 2：Bob also likes to play football games.
基于这两个文本文档，提取单个单词，并构造一个词典：
Dictionary = {1:”Bob”, 2. “like”, 3. “to”, 4. “play”, 5. “basketball”, 6. “also”, 7. “football”, 8. “games”, 9. “Jim”, 10. “too”}。
这个词典一共包含10个不同的单词，根据词典，对上面两个文档中的单词出现次数进行统计，每个文档可表示为10维向量。如下：
1：[1, 2, 1, 1, 1, 0, 0, 0, 1, 1] 2：[1, 1, 1, 1 ,0, 1, 1, 1, 0, 0]
若每种类型的文档中单词的直方图统计呈现特定的规律，则可以利用这种规律进行海量文档归类。
Bag Of Feature
1.1 [CVPR06] Beyond Bags of Features: Spatial Pyramid Matching for Recognizing Natural Scene Categories
摘要：将BOW的思想引入到图像中来，word在图像中用一种特定的特征描述子来代替，但这样完全忽略了图像的空间布局关系，incapable of capturing shape or of segmenting an object from its background，因此结合空间金字塔匹配来实现。 Our method involves repeatedly subdividing the image and computing histograms of local features at increasingly fine resolutions.
比较：以下三方面和传统方法比较：
1 locally orderless images：SPM as an alternative formulation of a locally orderless image, instead of a Gaussian scale space of apertures,define a fixed hierarchy of rectangular windows.
2 multiresolution histograms：fixing the resolution at which the features are computed, but varying the spatial resolution at which they are aggregated.
3 subdivide and disorder：the best subdivision scheme may be achieved when multiple resolutions are combined in a principled way; the reason for the empirical success of “subdivide and disorder” techniques is the fact that they actually perform approximate geometric matching.
Pyramid Match Kernels:
xy表示两个矢量 PyramidMatch用来计算xy之间的appriosimate correspondence.通过placing a sequence of increasingly coarser grids over the feature space and taking a weighted sum of the number of matches that occur at each level of resolution.
Match means they fall into the same cell. Resolution counts from 0 to L.
At level l,image can be divide into 2exp(d*l) cells(这里的cell应该就是后面的聚类中心？);The number of matchs at level l is given by (1);
The weight number of level l is set to 1/(2exp(L-l)),Note lower(coarser) level include the num of finer level, so the num of level l is given by 
.The Pyramid match kernel can be given by(2);
(1)
(2)
(1)为什么表示了xy之间的appriosimate correspondence？怎样计算H，如何算是fall into the same cell？
Spatial Matching Scheme
perform pyramid matching in the two-dimensional image space, and use traditional clustering techniques in feature space.(对于图像中feature空间，图像的坐标已经包含了几何空间信息，只需要按照坐标顺序排列vector即可)(特征空间用聚类将特征聚到M个类别channel，大概就是上面讲的fall into the same cell，H就是用直方图统计，I越小表示二者相关度越小)
The final dimension is:
(上式中k(x,y) 中并不是相加 而是每level的I矢量连接成一个很长的矢量) ; M=400 L=3 d=34000 is long and sparse.
Normalize all histograms by the total weight of all features in the image.
Q：
局部和全局特征表示：本文中说到SPM是一种approximate global geometric correspondence，又如何理解an alternative formulation of a locally orderless image,传统的局部和全局特征是怎样定义的，有哪些？？
ps：
部分来源于：http://blog.csdn.net/v_JULY_v
标签：style blog http ar io color os sp for
原文地址：http://www.cnblogs.com/oudan/p/4169021.html
