特征匹配算法

1、2 x 2 matrix of image derivatives (averaged inneighborhood of a point).（1）平移Translation（2）歐幾里德幾何（平移+旋轉）（3）相似性變換（平移+旋轉+尺度）（4）仿射變換（5）投影變換The need for invariance1. 幾何變換2. 光照變化),(),(),(),(),(),()(),(),(222HarrisDyDxDxDxDxDxIDDIDIIIIIIIGxxxxxxxxM2222221)()(*)(),(yxDDxegxIgxxI公式由來說明公式由來說明Wyxwwwwywwwwxwwww

2、yyxxIyxIyyxxIyxIyxf),(22),(),( ),(),(),(yxyxIyxIyxIyyxxIwwywwxwwww),(),(),(),(位移后影像函數(shù)通過一階泰勒展開式近似重新計算 f(x,y):yxyxyxyxIyxIyxIyxIyxyxyxIyxIyxfwwywwxWyxwwywwxWyxwwywwxwwwwM ),(),(),(),( ),(),(),(),(),(2“second moment matrix M”21),(2),(),(),(200),(),(),(),(),(),(WyxwwyWyxwwywwxWyxwwywwxWyxwwxwwwwwwwwyxIy

3、xIyxIyxIyxIyxIMM can be used to derive a measure of “cornerness”Independent of various displacements (x, y)Corner: significant gradients in 1 directions rank M = 2Edge: significant gradient in 1 direction rank M = 1Homogeneous region rank M = 0IMM tracedetHarriscxxxxIxxIxxITT)()()()(0000得到Hessian矩陣(

4、 ,)( ,)( ,)( ,)xxDxyDxyDyyDxxIxIxHIxIx其 中 ， I 是 高 斯 平 滑 函 數(shù) 的 二 階 偏 導 數(shù)2)det(xyyyxxIIIHIIxxIxyIyy The eigenvalues of M reveal the amount of intensity change in the two principal orthogonal gradient directions in the window.TXXM2100 n(2) The Laplacian-of-Gaussian (LoG) Detectorn(3) The Difference-of-

5、Gaussian (DoG) Detectorn(4) The Harris-Laplacian Detectorn(5) The Hessian-Laplace Detector),(.1xIfmii), (.1xIfmiin(2) The Laplacian-of-Gaussian (LoG) Detector 1 Laplacian filter Laplacian算子具有旋轉不變性，但對噪聲很敏感，因此常需進行平滑操作 2 LoG filter 高斯濾波平滑，然后拉普拉斯濾波。),(*),(),(*),(22yxIyxGyxGyxIIIyxIyxIyxIyyxx*010141010*1

6、21121),(),(),(2SmoothLaplacianI(x,y)O(x,y)22222),(yGxGyxGLaplacian-of-Gaussian (LoG)尺度空間的局部極大值點n(3) The Difference-of-Gaussian (DoG) Detector 可用高斯差分函數(shù)(DoG)近似LoG),(*),(),(),(yxIyxGkyxGyxD Original image 412Sampling withstep 4 4 =2 Computation in Gaussian scale pyramid0 :DoG0)()( :LoG21IGIGDIGIGLLowes

7、 DoG keypoints Lowe Edge zero-crossing Blob at corresponding scale: local extremum ! Low contrast corner suppression: threshold Assess curvature distinguish corners from edges Keypoint detection: DDDDDyyxyxyxxD ofmatrix Hessian HthDDHHdettrace2n(4) The Harris-Laplacian Detector 1 初始化：多尺度下的Harris角點檢測

8、 2 基于Laplacian的尺度選擇Harris pointsHarris-Laplacian pointsn(5) The Hessian-Laplace Detector 思想與Harris-Laplacian Detector相同圖：Hessian-Laplace算子應用于具有尺度改變的影像結果圖：Harris-Laplace算子在同一場景下不同尺度的兩幅影像上特征檢測結果，圓的半徑代表了特征尺度大小 給定一組由Harris-Laplace算子得到其尺度特征的初始點，用橢圓形區(qū)域獲得仿射不變性。具體處理步驟如下： (1)由Harris-Laplace算子獲得興趣點初始區(qū)域 (2)由二階

9、矩矩陣估計區(qū)域仿射形狀 (3)歸一化仿射區(qū)域成為圓形區(qū)域 (4)在歸一化的影像上重新檢測新的位置和尺度 (5)如果二階矩矩陣的特征值在新的點上不相等，則轉(2) 圖：利用二階矩矩陣的特征值估計興趣點區(qū)域的仿射形狀，變換是用該矩陣的平方根進行的，經(jīng)過歸一化的圖像XL和XR之間的變換是旋轉變換關系，只取決于一個旋轉因子，因子大小代表了特征值的比率圖：Harris-Affine算子檢測的從不同視角得到的結果圖 圖：Hessian-Affine算子得到的不同視圖下的影像檢測結果Harris-Laplace (HRL) scale-adapted Harris (rotation invariant)

10、Laplacian-of-Gaussian scale-space (scale invariant) detects cornerlike structuresn Hessian-Laplace (HSL) Hessian detector (rotation invariant) Laplacian-of-Gaussian scale-space (scale invariant) blob-like structures higher localization accuracy than DoG higher scale selection accuray than HRL Laplac

11、e kernel fits better to blobs than to cornersn Difference-of-Gaussian (DoG) local scale-space maxima of the DoG blob-like structures respond to edges (unstable)Harris-Affine (HRA) localization and scale estimated by HRL affine adaptation process based on second moment matrixn Hessian-Affine (HSA) HS

12、L + affine adaptation processIlluminationScaleRotationAffinePyaqpPxapqyxIyxm),(),()()( :,00010010yxIyyxxmmymmxqPxPyppqNormalized central moments Translation, rotation, scale invariant moments 1 . 7 HuGeometric/photometric, color invariants vanGool et al.21 with ,00qppqpq211202202022014)( Computing t

13、he invariants reduces the number of dimensions More suitable for color imagesNnRIXXLXIJniiN,.,0,),(),(),(.1 Which steer derivatives in a particular direction given the components of the local jet),()()(),(yxGiyxiyxyxKnmmn影像導數(shù)由高斯導數(shù)的卷積來獲得。(a)高斯導數(shù)到4階(b)6階復數(shù)濾波(complex filters)L(x,)是由高斯導數(shù)和影像卷積而成 旋轉不變Approximate SIFT Works almost equally well Very fastFast approximation of SIFT ideaEfficient computation by 2D box filters & integral images 6 times faster than SIFTEquivalent quality for object identification見后面講解K-d 樹樹Scale-space extrema detection2.2