What does "kernel based" mean?

Question

In my thesis I try to explain what kernel based methods are, especially the meaning for object detection.

I know kernel based methods like Mean- and CamShift and I know how to use them. I understand how the shift work. But: What does the kernel do, what does he describe?

I know, wikipedia have articles about kernels but I still don´t get it. :(

Q1: What could be an subset for an image?

Q2: How does the kernel project the points in an image?

Q3: Could you give me an simple example to understand kernels?

Thank you in advance!

Answer 1

In general, a kernel is a function that acts as a parameter to some algorithm.

Filtering: For example, it's possible to call the impulse response of a filter $h[n]$ a kernel, so that it is the parameter that defines the filter operation: $$ y[n] = h[n] * x[n]. $$

The use of the term kernel in the filtering context is much more common in 2D filtering or image processing. The link talks about the kernel being a matrix, but really it's just a sampling of the function that is the "true" kernel.

PDF Estimation: Kernel-based methods are often used in other contexts, too. For example, when estimating the probability density function of a random variable, kernel-based estimators are often preferable to simple histogramming. In that context, there are many different possible kernels.

Machine Learning: Finally, another context for kernel based algorithms is in machine learning. Here, we are interested in classification of an input into one of (possibly) many classes. Again, the kernel is a function $k(\mathbf{x}_i,\mathbf{x}')$ that parametrizes the algorithm and there are many possible selections.