# What does 'energy' in image processing mean?

I have been going through this paper: Seam Carving for Content-Aware Image Resizing which talks about resizing images by seam carving depending on the image energy or the energy function.

Some related quotes from the paper are:

A seam is a connected path of low energy pixels in an image

and

A seam is an optimal 8-connected path of pixels on a single image from top to bottom, or left to right, where optimality is defined by an image energy function

So, what does the 'energy' in an image mean, in this particular context?

PS: I have gone through this question, but the answers were very broad and vague because of this reason.

• are you familiar with the meaning of energy of a signal in signal processing? – Media Jan 31 '18 at 10:28
• @Media Not really. But, a google query landed me here. Is it correct? – Dawny33 Jan 31 '18 at 10:31
• yes, exactly, I don't know latex, otherwise I would answer :) just consider that image is a 2d signal, there is not much difference for extending the definitions in signal processing to image processing at least for this. – Media Jan 31 '18 at 10:33
• Also take a look at here for understanding the interpretation of the formula. – Media Jan 31 '18 at 10:34
• Gotcha! Thank you. Do try to answer. We have very helpful folks here who can fix your latex via edits anyway :) – Dawny33 Jan 31 '18 at 10:34

## 1 Answer

I quote from here which our friend has provided.

Energy in this context is not, strictly speaking, the same as the conventional notion of energy in physics and the other sciences. The two concepts are, however, closely related, and it is possible to convert from one to the other: where Z represents the magnitude, in appropriate units of measure, of the load driven by the signal.

Also for figuring out the interpretation of energy in this context you can see here.

After a while, I found a bit better explanation for energy as you can read the answers from here.

Energy is used to describe a measure of "information" when formulating an operation under a probability framework such as MAP (maximum a priori) estimation in conjunction with Markov Random Fields. Sometimes the energy can be a negative measure to be minimised and sometimes it is a positive measure to be maximized.

or you can read:

Energy is a fairly loose term used to describe any user defined function (in the image domain).

• Thank you. One last query: Would you call the hist plot I did here as the energy graph? – Dawny33 Jan 31 '18 at 10:45
• @Dawny33 sorry for late answer, actually I don't think so. The reason is simple. The signal is 2d, so its energy should be described in 2d dimension, at least as I know. Moreover, the histogram is more like probability of different densities in an image. Take a look at here. Let me know if you want more explanations. – Media Jan 31 '18 at 12:13
• @Dawny33 I don't know why I made the mistake but I meant intensity, not density :) – Media Jan 31 '18 at 14:30