Image analysis by moment invariants using a set of step-like basis functions

• Moment invariants are a well known and thoroughly tested method for image analysis.
• Zernike moments are among the sets of moments with better overall performance.
• The author proposes a new set of moments using discontinuous functions as basis.
• Tested in an image retrieval task, has reached the same result as Zernike moments.
• This results has been achieved using a description length 40% shorter than Zernike’s.

Moment invariants have been thoroughly studied and repeatedly proposed as one of the most powerful tools for 2D shape identification. In this paper a set of such descriptors is proposed, being the basis functions discontinuous in a finite number of points. The goal of using discontinuous functions is to avoid the Gibbs phenomenon, and therefore to yield a better approximation capability for discontinuous signals, as images. Moreover, the proposed set of moments allows the definition of rotation invariants, being this the other main design concern. Translation and scale invariance are achieved by means of standard image normalization. Tests are conducted to evaluate the behavior of these descriptors in noisy environments, where images are corrupted with Gaussian noise up to different SNR values. Results are compared to those obtained using Zernike moments, showing that the proposed descriptor has the same performance in image retrieval tasks in noisy environments, but demanding much less computational power for every stage in the query chain.