# Alignment

“First, ‘interest points’ are selected at distinctive locations in the image, such as corners, blobs, and T-junctions.  The most valuable property of an interest point detector is its repeatability, i.e. whether it reliably finds the same interest points under different viewing conditions.

Next, the neighbourhood of every interest point is represented by a feature vector. This descriptor has to be distinctive and, at the same time, robust to noise, detection errors, and geometric and photometric deformations.

Finally, the descriptor vectors are matched between the vectors, e.g. the Mahalanobis or Euclidean distance.  The dimension of this vector has a direct impact on the time this takes, and a lower number of dimensions is therefore desirable.” (Bay, Herbert et al. 2006. SURF: Speeded Up Robust Features)

Match the two vectors by comparing their distance (Euiclidean or Mahalanobis).

A homography is a little 3×3 matrix that tells us how to map one image (a set of pixel) onto another image. Once we have the key points and descriptors, we can find this matrix.

Here is the basic algorithm OpenCV’s implementation of SURF:
1. Use cvExtractSURF to get key points and descriptors from both images.
2. Find matching key points by comparing the distance between the key points. We will use a naive nearest neighbor approach.
3. Once the pairs of key points are found, stick them into cvFindHomography to get the homography matrix.
4. Use the homography to warp one image to the other.

Matching SIFT Using Nearest Neighbor

Matching points whose ratio (best_match_cost / second_best_match_cost) < 0.7

• Kdtree is just a way of finding nearby vectors quickly; it has little to do with what is being matched (vectors of numbers representing …), or how (Euclidean distance).
• Now kdtrees are very fast for 2d, 3d … up to perhaps 20d, but may be no faster than a linear scan of all the data above 20d. So how can a kdtree work for features in 128d ? The main trick is to quit searching early.
• The paper by Muja and Lowe, Fast approximate nearest neighbors with automatic algorithm configuration, 2009, 10p, describes multiple randomized kdtrees for matching 128d SIFT features. (Lowe is the inventor of SIFT.)
• using kd-trees for approximate NN search in higher dimensions:
• ## Experiments on Approximate Nearest-Neighbor Search using kd-Trees

RANSAC【RANdom SAmple Consensus（随机抽样一致性）】

RANSAC 的基本思想是在进行参数估计时，不是不加区分地对待所有可用的输入数据，而是首先针对具体问题设计出一个目标函数，然后迭代地估计该函数的参数值，利用这些初始参数值把所有的数据分为所谓的“内点”(Inliers，即满足估计参数的点)和“外点”(Outliers，即不满足估计参数的点)，最后反过来用所有的“内点”重新计算和估计函数的参数。

• Choose a small subset of points uniformly at random
• Fit a model to that subset a model to that subset
• Find all remaining points that are “close” to the model and reject the rest as outliers
• Do this many times and choose the best model this many times and choose the best model

Transform all the template Points to the target image – Affine Transformation

Point (x,y) is mapped to (u,v) by the linear function:

u = a x + b y + c
v = c x + d y + e

Mtalab code:

`t = cp2tform(src_points, target_points, ‘affine’);`

Other 2D transformations:

• Similarity(translation, scale, rotation)
• Homography: Fitting a plane projective transformation that
• between two views of a planar surface;
• between images from two cameras that share the same center

Hough transform

We want to find a template defined by its reference point (center) and several distinct types of landmark points in stable spatial configuration.

Detecting the template:
For each feature in a new image, look up that feature type in the Model look up that feature type in the model and vote for the possible center locations associated with that type in the model.

Application in recognition

Implicit shape models: Training

1. Build codebook of patches around extracted interest points using clustering
2. Map the patch around each interest point to closest codebook entry
3. For each codebook entry, store all positions it was found, relative to object center
4. Extract weighted segmentation mask based on weighted segmentation mask based on stored masks for the codebook occurrences

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