I am trying to understand how a simple image recognition of an image with dynamic size could work. What I have seen is that parts of the images are taken and evaluated. For example a simple finger recognition could be done turning the image grayscale, taking parts of the image and evaluating them. What I understand is how these parts are evaluated and how this could be done on an image with dynamic size ratio. Is a kernel function needed, or how do you proceed when you take the different parts of an image?
Normally we build a classifier that accepts images of a fixed size: say, 100x100 pixels. Given an image that is larger than that, we re-scale it to 100x100 pixels before feeding it into the classifier.
This is often combined with other techniques to locate where in a larger image the object is located. For instance, if you want to detect the presence of a bus in a picture, you build a classifier that recognizes a picture of a bus (where the bus fills the frame). Then, given a picture that might contain a bus and other stuff, you try cropping out different rectangles from within the image and feeding each one to the classifier. There are other more sophisticated techniques as well based on deep neural networks and regression.
To learn more, I suggest you read about object detection and object recognition. There's lots written about the subject in the research literature, and there are excellent tutorials available online. The state-of-the-art methods use deep neural networks.