SIFT Taylor Expansion确定亚像素位置 [英] SIFT Taylor Expansion working out subpixel locations

问题描述

我正在尝试实现SIFT，目前我只是想在开始在MATLAB中实现它之前了解它的工作原理，除了可以使用泰勒扩展来计算亚像素精度之外，我对它的理解程度很高:

I am trying to implement SIFT and am currently just trying to understand how it works before starting to implement it in MATLAB, i understand most of it except how to work out subpixel accuracy using Taylor Expansion:

上面是原始论文中的等式.我对如何应用有一些疑问.

Above is the equation from the original paper. I have a few question on how it is applied.

导数是否分别在每个维度上求出，然后将等式应用于x然后是y?

Are the derivatives worked out in each dimension seperatly and then the equation applied to x then y?

一阶和二阶导数是否也沿sigma轴应用?

Are the first and second derivates applied along the sigma axis aswell?

我在看以前的实现时已经很累了，但是无法找到他们在哪里实现. 预先感谢

I have tired looking at previous implementations but cannot seam to find where they do this. Thanks in advance

推荐答案

在我们的例子中，D是具有变量 x =(x，y，s)的体积函数，其中s是小数位数在八度.

In our case, D is a volumetric function with variables x = (x,y,s), where s is the scale in the octave.

问题:是否分别计算了每个维度的导数，然后将等式应用于x然后是y?

Question: Are the derivatives worked out in each dimension seperatly and then the equation applied to x then y?

答案:是否在各个维度上分别计算了导数?"是的，对于一阶导数，我们分别计算x，y和s的偏导数. 否，偏导数的结果将是一个长度为3的向量，我们将其乘以逆Hessian(3 X 3矩阵)即可计算出的子像素位置> x .

Answer: "Are the derivatives worked out in each dimension seperatly?" Yes, for the first derivative, we calculate the partial derivatives for x, y, and s separately. "the equation applied to x then y?", No, the result of the partial derivatives will be a vector of length 3, which we simply multiply it by the inverse Hessian (3 X 3 matrix) to calculate the subpixel position of x.

对于二阶导数，我们使用Hessian矩阵(在这种情况下为3X3矩阵).

For the second derivative, we use the Hessian Matrix (3X3 Matrix in this case).

问题:一阶和二阶导数是否也沿sigma轴应用?

Question: Are the first and second derivates applied along the sigma axis aswell?

答案是的，因为它表示3D空间中定义了D的轴.

Answer Yes, because it represents an axis in the 3D space, where D is defined.

注释:

• 有关数学上详尽的解释，请请参见
• 有关C ++中的代码，请参见.
• 为了计算离散域中的偏导数， 我们使用

• For mathematically elaborated explanation see
• For code in C++ see.
• In order to calculate the partial derivative in the discrete domain, we use the the finite differences.

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