Hello Every one I have been trying to understand the intuitive meaning of using a regularizer in images. Specifially what does the Total Variation regularizer prevent the edges in images?
Regularisation is similar to "normalisation" (i.e. - "rescaling" from 0 to 1 or 1 to 255 etc.) but it is also somehow different. When using regularisation, instead of using the “stretch” of the “normal scale" (say you have dynamic images that vary a lot and you “normalise” them by some average value.
Regularisation “works” similar to a local contrast: it uses an "adaptable" scale, the scale is usually defined according some mathematical function that "searches" for the local minimum value and "re-scale(s)" the image back by using “absolute values” of the differences between the differences of the maximum values in the images and the minimal values and that local minimum value.
The Local minimum would corresponds to the "0" (in the re-scaling from 0 to 1 in images) or to the "1" for the rescaling in "1" to "255" values in images.
I hope that I have helped you for better understand the intuitive side of the term.
Hi, are you asking about the regularization term that we use in the total variation algorithms? Regularizer is a common concept in optimization algorithm that helps you to find a suitable solution maintaining certain criteria. The regularization parameters try to make balance between the criteria- somewhat like a overfitting and underfitting problem. In total variation problems, we generally have a fidelity term and a smoothness regularizer.
Firstly I would like to thank you for the answers. However, I want to intuitively understand how does the total variation regularization preserves edges and at the same time does the smoothing / noise removal. Specifically in this paper http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.117.1675&rep=rep1&type=pdf
wherein the idea is to estimate the noise free image which closely matches the noisy image at the same time takes into account the total variation in the image as a regularizer. What I dont understand here is what does variation regularizer intuitively do to the image? Does it mean that for every pixel in the regularizer calculates the first order difference and tries to reduce the difference values in the image.
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