在前面的blog中，我們已經講了SIFT的原理，這裡我們再詳細講解SIFT的變體：PCA-SIFT和GLOH。
– Scale invariant feature transform (SIFT): Lowe, 2004.
– PCA-SIFT: SIFT: Ke and Sukthankar 2004 Ke and Sukthankar, 2004.
– Gradient location-orientation histogram (GLOH): Mikolajczyk and Schmid 2005
– SURF(Speeded Up Robust Features), Bay, 2006回顧前面講過的SIFT算法，可以很好地應對旋轉和尺度不變，光強不變，位置遮擋不變（http://blog.csdn.net/abcjennifer/article/details/7639681），其過程分為四步：
– Detection of scale-space extreme 建構尺度空間
– Accurate keypoint localization 關鍵點檢測
– Orientation assignment 指定方向
– The local image descriptor 局部圖像描述子
David G. Lowe, "Distinctive image features from scale-invariant keypoints," International Journal of Computer Vision, 60, 2 (2004), pp. 91-110
PCA(Principle component analysis) SIFT 描述子将在所有描述子中提取出更有區分度，更robust to image deformations的特征。其方法：
– 在第四步中，不用原先的4*4*8個描述子，而是在41*41的圖像塊上計算39*39*2（x,y方向）個梯度導數，然後使用PCA将得到的3042維向量降到36維。
Y. Ke and R. Sukthankar, “PCA-SIFT: A More Distinctive Representation for Local Image 15 Descriptors,” Computer Vision and Pattern Recognition, 2004.
當然，上圖隻是PCA-SIFT作者的一面之詞，Mikolajczyk and Schmid（2005）的描述子測評顯示還是SIFT比較靠譜。
Mikolajczyk and Schmid（2005）提出了一種SIFT變體的描述子，使用對數極坐标分級結構替代Lowe（2004）使用的4象限。空間上取半徑6，11，15，角度上分八個區間（除中間區域）,然後将272（17*16）維的histogram在一個大資料庫上訓練，用PCA投影到一個128維向量。
K. Mikolajczyk and C. Schmid,“A performance evaluation of local descriptors ,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 27, No. 10, pp. 1615-1630, Oct. 2005
SURF與SIFT稍有不同，
-SIFT建立一幅圖像的金字塔，在每一層進行高斯濾波并求取圖像差（DOG）進行特征點的提取，而SURF用的是hessian matrix黑森矩陣。
-SIFT特征建立圖像金字塔處理尺度不變特性，而SURF特征将高斯核近似為一個方波濾波，SURF金字塔僅僅用來作特征點的檢測。
下文來自《A Comparison of SIFT, PCA-SIFT and SURF》
SIFT and SURF algorithms employ slightly different ways of detecting features [9]. SIFT builds an image
pyramids, filtering each layer with Gaussians of increasing sigma values and taking the difference. On the
other hand, SURF creates a “stack” without 2:1 down sampling for higher levels in the pyramid resulting
in images of the same resolution [9]. Due to the use of integral images, SURF filters the stack using a box
filter approximation of second-order Gaussian partial derivatives, since integral images allow the
computation of rectangular box filters in near constant time [3].
In keypoint matching step, the nearest neighbor is defined as the keypoint with minimum Euclidean
distance for the invariant descriptor vector. Lowe used a more effective measurement that obtained by
comparing the distance of the closest neighbor to that second-closest neighbor [1] so the author of this
paper decided to choose 0.5 as distance ratio like Lowe did in SIFT.
Herbert Bay, Andreas Ess, Tinne Tuytelaars, Luc Van Gool "SURF: Speeded Up Robust Features", Computer Vision and Image Understanding (CVIU), Vol. 110, No. 3, pp. 346--359, 2008
ftp://ftp.vision.ee.ethz.ch/publications/articles/eth_biwi_00517.pdf
論文：A comparison of SIFT, PCA-SIFT and SURF 對三種方法給出了性能上的比較，源圖檔來源于Graffiti dataset，對原圖像進行尺度、旋轉、模糊、亮度變化、仿射變換等變化後，再與原圖像進行比對，統計比對的效果。效果以可重複出現性為評價名額。
對以上三種方法進行比較：
| method | Time | Scale | Rotation | Blur | Illumination | Affine |
| Sift | common | best | best | common | common | good |
| PCA-sift | good | good | good | best | good | best |
| Surf | best | common | common | good | best | good |
由此可見，SIFT在尺度和旋轉變換的情況下效果最好，SURF在亮度變化下比對效果最好，在模糊方面優于SIFT，而尺度和旋轉的變化不及SIFT，旋轉不變上比SIFT差很多。速度上看，SURF是SIFT速度的3倍。
采用最近鄰作為比對政策的特征描述子性能測評結果：
Reference:
http://blog.csdn.net/abcjennifer/article/details/7365651
http://www.cscjournals.org/csc/manuscript/Journals/IJIP/volume3/Issue4/IJIP-51.pdf
http://www.cnblogs.com/mysunnyday/archive/2011/08/31/2160298.html
http://140.115.156.251/vclab/teacher/2011AIP/Feature%20Detection%20and%20Matching%20(Part%20II).pdf