Distinctive Image Features from Scale-Invariant Keypoint 之学习笔记
Detection of Scale-Space Extrema
First stage of keypoint detection is to identify locations and scales that can be repeataby (repeatedly) assigned under differing views of the same object. Detecting locations that are invariant to scale change of the image can be accomplished by searching for stable features across all possible scales, using a continuous function of scale known as scale space.
找到关键点的第一步是：找到不同视图下同一个物体的可以重复赋值的位置和scales。查找对于在图像的scale变化下保持不变的位置可以通过查找所有可能的尺度下稳定的特征完成，使用一个叫做scale space（尺度空间）的连续函数完成。
The scale space of an image is defined as a function, L(x, y, σ), that is produced from the convolution of a variable-scale Gaussian, G(x, y, σ), with an input image, I(x, y)
图片的尺度空间被定义为一个函数，L(x, y, σ) = G(x, y, σ) * I(x, y)
To efficiently detect stable keypoint locations in scale space, using scale-space extrema in the difference-of-Gaussian function convolved with the image, D(x, y, σ), which can be computed by a constant multiplicative factor k:
D(x, y, σ) = (G(x, y, kσ) – (G(x, y, σ)) * I(x, y)
= L(x, y, kσ) – L(x, y, σ)
这样相减会得到尺度空间的极值。（blur radius 5 – blur radius 50）
There are a number of reasons for choosing this function. First, it is a particularly efficient function to compute, as the smoothed images, L, need to be computed in any case for scale space feature description, and D can therefore be computed by simple image subtraction.
有很多理由支撑我们选择这个函数。首先，它是一个特别有效的计算函数，因为Image L 要计算出尺度空间的特征描述符，D则能够用简单的图片相减得到。（前文SIFT中图片例子）
In addition, the difference-of-Gaussian function provides a close approximation to the scale-normalized Laplacian of Gaussian, σ2▽2G. Lindeberg showed that the normalization of the Laplacian with the factor σ2 is required for true scale invariance. Mikolaijczyk found that the maxima and minima of σ2▽2G produce the most stable image features compared to a range of other possible image functions, such as the gradient, Hessian, or Harris corner function.
Difference-of-Gaussian提供了一个近似于尺度标准化的Laplacian of Gaussian. Lindeberg证明要达到真正的scale 不变的话，需要使用σ2作为拉普拉斯标准化的算子。Mikolaijczyk则发现，使用σ2▽2G的极大值或极小值，与很多图像函数比较起来，它得到的图像特征值是最稳定的。
