# On the Realization and Analysis of Circular Harmonic Transforms for Feature Detection

## TL;DR

This paper introduces a novel approach to computing circular-harmonic spectra efficiently using radial apodization, enabling improved feature detection like corners in images, with practical application to airborne sensor data.

## Contribution

It presents a new method leveraging radial apodization for efficient circular-harmonic transforms, reducing complexity and mitigating discretization artifacts.

## Key findings

- Efficient computation of circular-harmonic spectra achieved.
- Effective detection and characterization of corners in real data.
- Reduced angular aliasing artifacts in spectral analysis.

## Abstract

Circular-harmonic spectra are a compact representation of local image features in two dimensions. It is well known that the computational complexity of such transforms is greatly reduced when polar separability is exploited in steerable filter-banks. Further simplifications are possible when Cartesian separability is incorporated using the radial apodization (i.e. weight, window, or taper) described here, as a consequence of the Laguerre/Hermite correspondence over polar/Cartesian coordinates. The chosen form also mitigates undesirable discretization artefacts due to angular aliasing. The possible utility of circular-harmonic spectra for the description of simple features is illustrated using real data from an airborne electro-optic sensor. The spectrum is deployed in a test-statistic to detect and characterize corners of arbitrary angle and orientation (i.e. wedges). The test-statistic considers uncertainty due to finite sampling and clutter/noise.

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Source: https://tomesphere.com/paper/1907.12165