Physical Significance of Kurtosis in image

Hi

I am working on image texture analysis, I am trying to understand image Kurtosis. THere are different ways to interpret the value, Can you guys help me to understand physical significance, what does the value of the kurtosis value tell about a image.

Thanks

Answer 1

[Image Analyst]

Kurtosis is how "box-like" the histogram is. A kurtosis greater (I think) than 0 has a rather flat top and steep tails that are far away from the middle, king of like a rounded rectangle. A kurtosis less than 0 has a histogram that is rather spike-like with a tall central spike and long, low, rather flat tails.

A positive kurtosis image would have a fairly uniform distribution of gray levels but not too many at the extreme values, while a negative kurtosis image would have mid-level gray levels that are fairly dominant (that's what the central spike represents) and an otherwise uniform distribution (for gray levels away from the mid-gray level).

See my code for calculating skew and kurtosis in http://www.mathworks.com/matlabcentral/answers/15307-image-operations-skewness-and-kurtosis, along with an adidtional explanation.

[ram m]

i have referred the following link

http://www.image-engineering.de/index.php?option=com_content&view=article&id=558:what-is-kurtosis&catid=97:technotes-artikel

which says higher the value of kurtosis the more peaked the histogram is.

And it also give some relation with noise of a image, which I couldn't understand properly, Can you tell me how kurtosis is related to noise.

Thanks

[ram m]

the histogram in the link is wrt to mean adjusted values.

[Image Analyst]

Like I said, and the web page says, the higher the kurtosis the more pixels will have the dominant gray level and fewer pixels with other gray levels, thus it's more uniform and has lower noise. An infinite kurtosis would be a spike (delta function), and you can see it would be zero because the standard deviation for such a distribution is zero, so in that extreme you would have only one gray level and no noise at all.

[ram m]

Thank you for the explanation Sir