Step1: BBF算法，在KD-tree上找KNN。第一步做匹配咯~
1. 什么是KD-tree（from wiki）
K-Dimension tree，实际上是一棵平衡二叉树。
一般的KD-tree构造过程：
function kdtree (list of points pointList, int depth)
{
if pointList is empty
return nil;
else {
// Select axis based on depth so that axis cycles through all valid values
var int axis := depth mod k;
// Sort point list and choose median as pivot element
select median by axis from pointList;
// Create node and construct subtrees
var tree_node node;
node.location := median;
node.leftChild := kdtree(points in pointList before median, depth+1);
node.rightChild := kdtree(points in pointList after median, depth+1);
return node;
}
}
【例】pointList = [(2,3), (5,4), (9,6), (4,7), (8,1), (7,2)] tree = kdtree(pointList)
2. BBF算法，在KD-tree上找KNN ( K-nearest neighbor)
BBF(Best Bin First)算法，借助优先队列（这里用最小堆）实现。从根开始，在KD-tree上找路子的时候，错过的点先塞到优先队列里，自己先一个劲儿扫到leaf；然后再从队列里取出目前key值最小的（这里是是ki维上的距离最小者），重复上述过程，一个劲儿扫到leaf；直到队列找空了，或者已经重复了200遍了停止。
Step1: 将img2的features建KD-tree; kd_root = kdtree_build( feat2, n2 );。在这里，ki是选取均方差最大的那个维度，kv是各特征点在那个维度上的median值，features是你率领的整个儿子孙子特征大军，n是你儿子孙子个数。
|
Step2: 将img1的每个feat到KD-tree里找k个最近邻，这里k=2。
k = kdtree_bbf_knn( kd_root, feat, 2, &nbrs, KDTREE_BBF_MAX_NN_CHKS );
|
对“有意义的点”的解释：
|
Step3: 如果k近邻找到了(k=2)，那么判断是否能作为有效特征，d0/d1<0.49就算是咯~
|
Step2: 通过RANSAC算法来消除错配，什么是RANSAC先？
1. RANSAC (Random Sample Consensus, 随机抽样一致) (from wiki)
该算法做什么呢？呵呵，用一堆数据去搞定一个待定模型，这里所谓的搞定就是一反复测试、迭代的过程，找出一个error最小的模型及其对应的同盟军（consensus set）。用在我们的SIFT特征匹配里，就是说找一个变换矩阵出来，使得尽量多的特征点间都符合这个变换关系。
算法思想：
input:
data - a set of observations
model - a model that can be fitted to data
n - the minimum number of data required to fit the model
k - the maximum number of iterations allowed in the algorithm
t - a threshold value for determining when a datum fits a model
d - the number of close data values required to assert that a model fits well to data
output:
best_model - model parameters which best fit the data (or nil if no good model is found)
best_consensus_set - data point from which this model has been estimated
best_error - the error of this model relative to the data
iterations := 0
best_model := nil
best_consensus_set := nil
best_error := infinity
while iterations < k //进行K次迭代
maybe_inliers := n randomly selected values from data
maybe_model := model parameters fitted to maybe_inliers
consensus_set := maybe_inliers
for every point in data not in maybe_inliers
if point fits maybe_model with an error smaller than t //错误小于阈值t
add point to consensus_set //成为同盟，加入consensus set
if the number of elements in consensus_set is > d //同盟军已经大于d个人，够了
(this implies that we may have found a good model,
now test how good it is)
better_model := model parameters fitted to all points in consensus_set
this_error := a measure of how well better_model fits these points
if this_error < best_error
(we have found a model which is better than any of the previous ones,
keep it until a better one is found)
best_model := better_model
best_consensus_set := consensus_set
best_error := this_error
increment iterations
return best_model, best_consensus_set, best_error
2. RANSAC去除错配：
H = ransac_xform( feat1, n1, FEATURE_FWD_MATCH, lsq_homog, 4, 0.01,homog_xfer_err, 3.0, NULL, NULL );
|
思考中的一些问题：
features间的对应关系，记录在features->fwd_match里（matching feature from forward
imge）。
1. 数据是nm个特征点间的对应关系，由它们产生一个3*3变换矩阵（xform_fn = hsq_homog函数，此要>=4对的对应才可能计算出来咯~），此乃模型model。
2. 然后开始找同盟军（find_consensus函数），判断除了sample的其它对应关系是否满足这个模型（err_fn = homog_xfer_err函数，<=err_tol就OK~），满足则留下。
3. 一旦大于当前的in_max，那么该模型就升级为目前最牛的模型。（最最原始的RANSAC是按错误率最小走的，我们这会儿已经保证了错误率在err_tol范围内，按符合要求的对应数最大走，尽量多的特征能匹配地上）
4. 重复以上3步，直到(1-wm)k <=p_badxform (即0.01)，模型就算找定~
5. 最后再把模型和同盟军定一下，齐活儿~
声明：以上代码参考Rob Hess的SIFT实现。
