what will be the range of fractal dimension for 2 dimension binary image?

what will be the range of fractal dimension for 2 dimension binary image?

[dpb]

[-Inf Inf]

[Image Analyst]

Wouldn't it be between 1 and 2?

[dpb]

'Pends on whether it represents a fractal set or not...realistically, yes, it'll likely actually have a value at or near the Euclidean dimensionality, but the query as posed is, I think, indeterminate.

[Image Analyst]

I thought it was something like, if it was a straight line the fractal dimension would be 1. Then as the line wiggles and gets more tortuous, the fractal dimension gets larger and larger until it reaches 2 when the line is so tortuous that it completely fills the 2D plane. But I'm not an expert on fractals so that's just my very rudimentary understanding of it.

[dpb]

That's the basic idea, yeah...since the OP did limit his question to 2D I reacted too quickly I suppose. The image could have been from a higher dimension construct, but once it was projected into 2D its maximum is restricted to the topological dimension.

[Dhandapani.S]

Thank you both. i am in the process of offline handwritten signature verification. i tried the code given by Alceu Ferraz Costa. it Returns the Haussdorf fractal dimension of an object represented by the binary image. i get values like 0.48 0.05 for various signatures like the one in the aatchment. please help. will the fractal dimension be less than 0.

[Image Analyst]

I don't know that person, paper, or algorithm. I've never heard of a fractal dimension that is negative.

[Dhandapani.S]

herewith i am attaching the code file of his. i will be helpful if i got to know the fractal dimension of the signature attached.

Answer 1

[Image Analyst]

I believe it ranges from 1 to 2.

[dpb]

I think possible range would be [0 2]; the image could be a point

[Image Analyst]

True.