Derivative of this bicubic interpolation kernel

In summary, the individual is having trouble deriving the derivative kernel for the bicubic kernel and is seeking assistance from others. They have searched online and tried to use a program to help, but are still struggling with the process.
  • #1
pamparana
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Hello everyone,

I am using the bicubic kernel described here ( http://en.wikipedia.org/wiki/Bicubic_interpolation#Bicubic_convolution_algorithm ) to interpolate my image after applying some transformations.

I an using the matrix kernel described here with a = -0.5.

Now, what I also need to do is estimate the kernel that is the derivative of this bicubic kernel. There is a bit of discussion in this page on the derivative but I am finding it impossible to be able to derive this kernel.

I would be really grateful if someone can help me derive this derivative kernel. My calculus skills are quite rusty but this is a roadblock for me for quite a few days now. I have also searched high and low on the internet for this derivative kernel but to no avail.

I look forward to any assistance you can give me.

Luc
 
Physics news on Phys.org

1. What is a bicubic interpolation kernel?

A bicubic interpolation kernel is a mathematical function used to estimate values between known data points in a two-dimensional grid. It is commonly used to increase the resolution of an image or to smooth out data points.

2. How is the bicubic interpolation kernel calculated?

The bicubic interpolation kernel is calculated by taking a weighted average of the surrounding data points. This is typically done using a 4x4 grid of points, with the center point being the point of interest and the surrounding points being used to estimate its value.

3. What is the purpose of using a bicubic interpolation kernel?

The purpose of using a bicubic interpolation kernel is to improve the visual quality of an image or to create a smoother representation of a data set. It can also be used to increase the size of an image without losing too much detail.

4. How does the bicubic interpolation kernel differ from other interpolation methods?

The bicubic interpolation kernel differs from other interpolation methods in that it takes into account not only the four nearest data points, but also the surrounding points in a 4x4 grid. This allows for a more accurate estimation of values between data points.

5. Are there any limitations to using a bicubic interpolation kernel?

Yes, there are some limitations to using a bicubic interpolation kernel. It may not work well with irregularly spaced data, and it can also introduce artifacts or blurring in some cases. Additionally, it may not always accurately represent sharp changes or edges in the data.

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