3D image gradient in OpenCV

2
votes

I have a 3D image data obtained from a 3D OCT scan. The data can be represented as I(x,y,z) which means there is an intensity value at each voxel.

I am writing an algorithm which involves finding the image's gradient in x,y and z directions in C++. I've already written a code in C++ using OpenCV for 2D and want to extend it to 3D with minimal changes in my existing code for 2D.

I am familiar with 2D gradients using Sobel or Scharr operators. My search brought me to this post, answers to which recommend ITK and Point Cloud Library. However, these libraries have a lot more functionalities which might not be required. Since I am not very experienced with C++, these libraries require a bit of reading, which time doesn't permit me. Moreover, these libraries don't use cv::Mat object. If I use anything other than cv::Mat, my whole code might have to be changed.

Can anyone help me with this please?

Update 1: Possible solution using kernel separability

Based on @Photon's answer, I'm updating the question.

From what @Photon says, I get an idea of how to construct a Sobel kernel in 3D. However, even if I construct a 3x3x3 cube, how to implement it in OpenCV? The convolution operations in OpenCV using filter2d are only for 2D.

There can be one way. Since the Sobel kernel is separable, it means that we can break the 3D convolution into convolution in lower dimensions. Comments 20 and 21 of this link also tell the same thing. Now, we can separate the 3D kernel but even then filter2D cannot be used since the image is still in 3D. Is there a way to break down the image as well? There is an interesting post which hints at something like this. Any further ideas on this?

1
c++opencvimage-processing3d
Just write your own implementation of the filter, it's not that complicated. For each voxel (perhaps except the edges, up to you), calculate its Gx,Gy,Gz and store the output. Should be a few dozen lines of code at most. - Photon
To compute Gx, Gy or Gz, there are 2 options. One is to loop through every voxel which would be inefficient. Other way is convolution. But convolution using filter2D is possible only with 2D images. So, do you mean that I follow the loop based approach? - Ruchir
The convolution does the same loop inside. Perhaps a little more efficiently than you may do at first try, but it's basically the same. If it's time critical, you can later try to optimize using SIMD or GPU. - Photon
you may also calculate the gradient of xyz according to x + 1 - 1, y + 1 - 1 and z + 1 - 1, if this precision fufill your requirement. - Summer Sun

1 Answers

1
votes

Since the Sobel operator is separable, it's easy to envision how to add a 3rd dimension.

For example, when you look at the filter definition for Gx in the link you posted, you see that is multiplies the surrounding pixels by coefficients that have a sign dependent on the relative X position, and magnitude relative to the offset in Y.

When you extend to 3D, the Gx gradient should be calculated the same way, but you need to work on a 3x3x3 cube, and the coefficient sign remains the same definition, and the magnitude now depends on change in either Y or Z or both.

The other gradients (Gy, Gz) are the same but around their axis.