What Are Invariant Moments in 2D Images?

[butling]

Hi there

I'm thinking about using the rotation invarient moments by Hu/Flusser (http://en.wikipedia.org/wiki/Image_moment#Rotation_invariant_moments).

I'm a physicist by trade, with exceptionally poor math..! I'm not comfortable with exactly what these invariants are. The wikipedia link describes the first as the moment of inertia of the image, while the final one is the skew, but doesn't describe any others.

Is there an intuitive describtion of them, or are they just arbritary statistical measures of the image?

 

[Future Bruno]

Is there a reason why they're rotation invariant? Also, beyond 7 moments, is there any point in going further? Thanks for your help!

 

[quicknote]

Hello,

Invariant moments of 2D images are mathematical measures used to characterize the shape and structure of an image. They are called "invariant" because they remain the same regardless of the image's orientation or scale. These moments are used in image processing and computer vision applications, such as object recognition and image matching.

The first few moments, including the moment of inertia and skew, are used to describe the overall shape and orientation of the image. Higher order moments capture more detailed information about the image, such as its curvature and symmetry. They can also be used to distinguish between different types of shapes, such as circles, squares, and triangles.

While these moments may seem arbitrary, they are actually based on well-defined mathematical principles and have been shown to be effective in characterizing complex images. Overall, they provide a quantitative way to describe and compare images, which can be useful in various scientific and technological fields. I would recommend consulting with a mathematician or further studying the principles behind these moments to gain a better understanding of their significance.