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经典论文学习bag of feature(二)

Bag-of-word

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

 

 

经典论文学习bag of feature(二)