Detecting Curves in Very Noisy Images Using Fourier-Argand Moments

Detection of curves (e.g., ridges) from very noisy images is an important yet challenging task in photon-starved imaging applications (e.g., nuclear imaging modalities, fluorescence/electron microscopy, radioastronomy, first photon/light-in-flight imaging).In this paper, we exploit the consistency of the image along the curve, i.e., the fact that the image changes slowly when we move along the curve-"locally" laminar images. We compute a sequence of complex scalars that we call Fourier-Argand moments, and show that the direction of variation of a laminar image is purely encoded in the phase of these moments. In particular, focusing on ridges located at the center of the image, we show that using these moments altogether in a frequency estimation algorithm provides a very accurate and highly robust estimate of the direction of the ridge: we demonstrate this accuracy for noise levels as high as -10dB.We then show how to detect curves-i.e., local ridges-by computing the Fourier Argand moments within a sliding window across the image, and design a consistency map whose thresholding allows to keep only the pixels on the curve.Numerical experiments on both synthetic images and real images (low light photography) demonstrate the accuracy and robustness to noise of the proposed method, compared to a state of the art method.