A New Scheme for Robust Gradient Vector Estimation in Color Images

Abstract

Gradient estimators are mostly designed to yield accurate and robust estimates of the gradient magnitude, not the gradient direction. This paper proposes a method for the accurate and robust estimation of both the gradient magnitude and direction. It robustly estimates the gradient in the x- and y-directions. The robustness against noise is achieved by prefiltering and postfiltering of the gradient in each direction. To reduce edge blurring effects introduced by these filters, the gradient in a certain direction is obtained by applying the prefilter and postfilter in the perpendicular direction. The basic elements employed in each window are: highpass, lowpass and aggregation operators. The highpass operator is used as a gradient estimator, the lowpass operator is for prefiltering and postfiltering, and the aggregation operator is for aggregating the prefiltered and postfiltered gradients. Four different combinations of highpass, lowpass and aggregation operators are proposed: MVD-Median-Mean, MVD-Median-Max, RCMG-Median-Mean, and RCMG-Median-Max. Experimental results show that the RCMG-Median-Mean has the best performance in estimating the gradient and detecting the edges in noisy color images. It is computationally more efficient than the state-of-the-art gradient estimators and is able to accurately estimate the gradient direction as well as the gradient magnitude. Computer simulation results show that the proposed method outperforms other recently proposed color gradient estimators and edge detectors.

An Efficient Color Edge Detection Using the Mahalanobis Distance

“…In most 2 cases, a color distance (also known as gradient magnitude) is measured by the Euclidean distance of two vectors. The two schools of vector-based approaches are the gradient magnitudebased approach and the gradient vector-based approach [6].…”

“…On the contrary, the human perception of colors is more closely related to how the HSV color model views colors [6]. The HSV model separates the hue component that represents the dominant color from the saturation and lightness (value) components.…”

“…The key idea is to efficiently measure a color distance using a statistical distance, such as the Mahalanobis distance, which allows us to consider the hue, saturation, and lightness separately. This method is robust against the change of lightness as compared to previous methods that employ the Euclidean distance in measuring color distances [6][7][8][9][10][11][12]. Additionally, we propose a new technique to reduce the errors that are due to high frequencies of noisy pixels.…”

New Families of Fourier Eigenfunctions for Steerable Filtering

“…The main difficulty when computing the gradient of an image is that, as well known, it is an ill-posed problem, as infinitesimal perturbations of the input image may produce large variations of its gradient. Therefore, several regularization techniques have been developed to reliably estimate the image gradient (see, e.g., [35] for a survey) and the subject is still a fertile area of ongoing research [46], [47]. The classical approach to estimate the gradient is to convolve the input with the gradient of an isotropic Gaussian kernel [4].…”

Automatic movie restoration based on wave atom transform and nonparametric model

“…We use a vertical 5 × 5 Sobel detector to find where scratches are likely to appear and get a mask matrix M. To ensure an accurate scratch detection, morphological dilation operation [29] is applied to M. Besides Sobel detector, there exists many other effective edge and ridge detector, such as the method in [30]. However, considering the requirement for processing a large volume of data real-time, we apply the simple strategy.…”