图像检索知识整理
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1. SIFT特征提取
1.1 尺度空间生成
L ( x , y , σ ) = G ( x , y , σ ) ∗ I ( x , y ) L(x,y,\sigma) = G(x,y,\sigma) *I(x,y)L (x ,y ,σ)=G (x ,y ,σ)∗I (x ,y )
G ( x , y , σ ) = 1 2 π σ 2 e − ( x 2 + y 2 ) 2 σ 2 G(x,y,\sigma) = \frac{1}{2\pi\sigma^2}e^{\frac{-(x^2+y^2)}{2\sigma^2}}G (x ,y ,σ)=2 πσ2 1 e 2 σ2 −(x 2 +y 2 )
1.2 检测尺度空间极值点
1.3 精确定位极值点
D ( x , y , σ ) = D ( x , y , σ ) + ∂ D T ∂ x x + 1 2 x T ∂ 2 D ∂ x 2 D(x,y,\sigma) = D(x,y,\sigma)+\frac{\partial D^T}{\partial x}x+\frac{1}{2}x^T\frac{\partial^2 D}{\partial x^2}D (x ,y ,σ)=D (x ,y ,σ)+∂x ∂D T x +2 1 x T ∂x 2 ∂2 D
求导得：
x ^ = − ∂ 2 D − 1 ∂ x ∂ D ∂ x \hat x =-\frac{\partial^2 D^{-1}}{\partial x}\frac{\partial D}{\partial x}x ^=−∂x ∂2 D −1 ∂x ∂D
1.4 为每个关键点指定方向参数
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m ( x , y ) = ( L ( x + 1 , y ) − L ( x − 1 , y ) ) 2 + ( L ( x , y + 1 ) − L ( x , y − 1 ) ) 2 m(x,y)=\sqrt{(L(x+1,y)-L(x-1,y))^2+(L(x,y+1)-L(x,y-1))^2}m (x ,y )=(L (x +1 ,y )−L (x −1 ,y ))2 +(L (x ,y +1 )−L (x ,y −1 ))2
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1.5 关键描述子生成
以特征点为中心取 8 * 8的领域作为采样窗口，将采样点与特征点相对方向归入。
最后得到 8 * 8 *8的向量转换 [1, 128] 向量的描述子。
2. 匹配方法:词袋模型（BOW)
词袋模型（Bag of Words），是通过计算特征词频，利用词频反映图像全局特征，用于后续匹配的方法。对SIFT特征点放在一起进行聚类，得到代表性聚类中心（单词）、做词频统计（Term frequency)统计。
TF：词频统计
IDF：做完词频TF统计后，为了降低停用词带来的干扰，可以再算上个逆文档词频IDF，给TF乘上一个权重。
然后L2归一化，用内积做相似性度量。
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; 3.Fisher Vector
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L ( x ∣ λ ) = ∑ t = 1 T l o g p ( x t ∣ λ ) L(x|\lambda)=\sum_{t=1}^{T}{logp(x_t|\lambda)}\L (x ∣λ)=t =1 ∑T l o g p (x t ∣λ)
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y t i = w i u i ( x t ) ∑ j = 1 K w j u j ( x t ) y_{t_i}=\frac{w_iu_i(x_t)}{\sum_{j=1}^{K}{w_ju_j(x_t)}\}y t i =∑j =1 K w j u j (x t )w i u i (x t )
∂ L ( x ∣ λ ) ∂ w i = ∑ t = 1 T [ y t ( i ) w i − y t ( 1 ) w 1 ] , f o r i ≥ 2 \frac{\partial L(x|\lambda)}{\partial w_i} =\sum_{t=1}^{T}{[\frac{y_t(i)}{w_i}-\frac{y_t(1)}{w_1}]}, for i\ge2\∂w i ∂L (x ∣λ)=t =1 ∑T [w i y t (i )−w 1 y t (1 )],f o r i ≥2
∂ L ( x ∣ λ ) ∂ u i d = ∑ t = 1 T y t ( i ) [ x t d − u i d ( σ i d ) 2 ] \frac{\partial L(x|\lambda)}{\partial u_i^d} =\sum_{t=1}^{T}y_t(i){[\frac{x_t^d-u_i^d}{(\sigma_i^d)^2}]}\∂u i d ∂L (x ∣λ)=t =1 ∑T y t (i )[(σi d )2 x t d −u i d ]
∂ L ( x ∣ λ ) ∂ σ i d = ∑ t = 1 T y t ( i ) [ x t d − u i d ( σ i d ) 3 − 1 σ i d ] \frac{\partial L(x|\lambda)}{\partial \sigma_i^d} =\sum_{t=1}^{T}y_t(i){[\frac{x_t^d-u_i^d}{(\sigma_i^d)^3}-\frac{1}{\sigma_i^d}]}\∂σi d ∂L (x ∣λ)=t =1 ∑T y t (i )[(σi d )3 x t d −u i d −σi d 1 ]
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Original: https://blog.csdn.net/qq_32097577/article/details/109495157
Author: 潜沉10
Title: 图像检索知识整理（传统方法）
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