# Relation between entropys of spatial and frequency domain

• Chriszz
In summary, the speaker is discussing their efforts to measure the entropy of visual data, specifically images and videos. They mention using the Discrete Cosine Transform (DCT) to transform the data into the frequency domain and measuring the entropy using probability density functions (pdfs) for each AC component. However, when they measured the entropy over the spatial domain (pixels), it was different from the entropy in the frequency domain. They are seeking information on the relationship between the entropy of spatial and frequency domains, such as Parseval's theorem, but have not found it in textbooks or online. They are requesting comments on this relationship.
Chriszz
Dears,

I wish to measure the entropy of visual data such as image and video.
I did transform these image and videos into frequency domain such as DCT, then measured the entropy with these pdfs for each AC components of image and videos.

However, when I measured the entropy over spatial domain such as pixel, this entropy is differ to the entropy from DCT domain.

What is the relationship between the entropy of spatial and frequency domains? (Such as Parseval's theorem)
I couln't find this relation in the textbook for signal processing or the google.

Thanks!

Last edited:

## 1. What is entropy in the spatial domain?

Entropy in the spatial domain refers to the amount of disorder or randomness present in a signal or image. It is a measure of how unpredictable or varied the pixel values are in a given area or region.

## 2. How is entropy calculated in the frequency domain?

In the frequency domain, entropy is calculated by first transforming the signal or image from the spatial domain to the frequency domain using techniques such as Fourier transforms. Then, the entropy is calculated based on the distribution of frequencies present in the signal.

## 3. Is there a relationship between entropy in the spatial and frequency domains?

Yes, there is a direct relationship between entropy in the spatial and frequency domains. Generally, as the entropy increases in the spatial domain, it also increases in the frequency domain, indicating a higher level of disorder or variability in the signal.

## 4. How does entropy in the frequency domain affect image quality?

In image processing, entropy in the frequency domain is often used as a measure of image quality. A higher entropy in the frequency domain indicates a wider range of frequencies present in the image, which can result in better image quality and more details being captured.

## 5. Can entropy in the spatial and frequency domains be used to classify images?

Yes, entropy in the spatial and frequency domains can be used as features for image classification. By comparing the entropy values of different images, we can determine the level of disorder or variability present, which can aid in classifying images into different categories.

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