Scale invariance and noise in natural images

Abstract

Natural images are known to have scale invariant statistics. While some eariler studies have reported the kurtosis of marginal bandpass filter response distributions to be constant throughout scales, other studies have reported that the kurtosis values are lower for high frequency filters than for lower frequency ones. In this work we propose a resolution for this discrepancy and suggest that this change in kurtosis values is due to noise present in the image. We suggest that this effect is consistent with a clean, natural image corrupted by white noise. We propose a model for this effect, and use it to estimate noise standard deviation in corrupted natural images. In particular, our results suggest that classical benchmark images used in low-level vision are actually noisy and can be cleaned up. Our results on noise estimation on two sets of 50 and a 100 natural images are significantly better than the state-of-the-art.

Harmonic Variance: A Novel Measure for In-focus Segmentation

“…(7), we have σ 2 η (x 1 ) σ 2 η (x 2 ), which is inconsistent with our previous assumption. This explains that why the kurtosis estimation in [21,33] fails for low DoF images and their quadratic formulation shifts high frequency of the latent image into noise variance estimations.…”

“…As we show next, the noise variance estimation algorithms in [21,33] are limited and do not apply to low DoF images.…”

“…whereκ m (x) and κ m (x) represent the kurtosis value of the latent and the noisy I m at x for channel m. For natural images, kurtosis has the concentration property in the bandpass filtered domains, thus, the kurtosis of an image across the bandpass filtered channels can be approximated by a constant κ(x) ≈κ m (x) [21,33]. In other words, we can estimate the optimal local noise variance σ 2 η (x) and the kurtosis κ by designing a simple least squares minimization problem as…”

Automatic Highly Accurate Estimation of Gaussian Noise Level in Digital Images Using Filtration and Edges Detection Methods

“…Statistical approaches (SA) [6] are based on filtration of images and calculation of kurtosis values, which depends on the noise level. The accuracy of the methods decreases with the presence of textures in the images.…”

A Novel Image Noise Level Function Estimation Approach using Camera Response Function Constraint

“…Estimating the noise level from a single image is a significant task in many computer vision algorithms, especially for de-noising and forensic applications. Most algorithms [1][2] use the additive white Gaussian noise (AWGN) model, and generate noisy images by adding white noise manually into noise-free images in the experiments. However, the AWGN conjecture may not hold for real-life digital photographs because the actual CMOS/CCD sensor noise is strongly dependent on the light intensity, and the forgery makers are unlikely to deliberately add noise to lower the visual quality of the fake images.…”