Robust edge detector based on anisotropic diffusion-driven process

https://doi.org/10.1016/j.ipl.2015.12.003Get rights and content

Highlights

  • •

    We propose an alternative diffusion-driven edge detector for noisy images.

  • •

    The method is iterative, and includes a robust feature-dependent diffusivity.

  • •

    We describe the mechanics of the method and its strength to extract useful details.

  • •

    Comparisons with some traditional methods demonstrate that our method is superior.

  • •

    Finally, future research directions are provided.

Abstract

Edge detection involves a process to discriminate, highlight, and extract useful image features (edges and contours). In many situations, we prefer an edge detector that distinguishes these features more accurately, and which comfortably deals with a variety of data. Our observations, however, discovered that most edge-defining functionals underperform and generate false edges under poor imaging conditions. Therefore, the current research proposes a robust diffusion-driven edge detector for seriously degraded images. The method is iterative, and suppresses noise while simultaneously marking real edges and deemphasizing false edges. The anisotropic nature of the new functional helps to remove noise and to preserve semantic structures. Even more importantly, the functional exhibits a forward–backward behavior that may sharpen and strengthen edges. Comparisons with some other classical approaches demonstrate superiority of the proposed approach.

Introduction

Edges in an image are regions with rapidly changing intensity values. Extracting these critical features forms an important step in many computer vision applications, such as industrial automation and control, and has been an interesting and challenging research question for years [1], [2], [3], [4].

Humans are naturally equipped with senses to read, understand, and distinguish regions in the image (edges, contours, and flats). This is, however, a non-straightforward task for machines. Most machine-steered classical edge detectors underperform when input images are noisy, highly textured, or contain weak edges [3], [5], [6], [7]. We should note that real-world scenes usually suffer from noise and other unwanted artifacts, thus prompting for robust and more effective segmentation methods to extract meaningful features.

In this letter, we propose an alternative edge detection approach based on anisotropic diffusion processes. The new method is iterative, and includes a robust feature-sensitive edge detector. In flat regions, the formulation follows isotropic diffusion that suppresses noise; and near edges, the detector gradually declines smoothing and highlights semantic features. The process is iterative and automatic, which helps the model to efficiently and robustly capture true edges in worse imaging conditions. The intriguing property of the proposed edge detector, which differentiates it from some other classical methods, is its ability to treat severely degraded scenes and reject false edges. The new algorithm is simple and contains repetitive operators that can promote parallel computing in a real hardware.

Section snippets

Proposed diffusion-driven edge detector

Detecting edges and contours is perhaps the most critical step in almost all computer vision tasks. Before interpreting and analyzing real objects, machines need to precisely locate and register details of important features. To this end, several edge detectors have been proposed in the literature, with the classical ones being Canny, Sobel, Prewitt, and LoG (Laplacian of Gaussian). Despite their convincing performance, we noted from experimental results that the methods collapse for noisy

Numerical implementation

We used a four-point neighborhood explicit scheme (Fig. 1) to implement our model. Unlike implicit schemes like adaptive operator splitting, which include relatively harder implementation strategies, explicit schemes are simpler, computationally efficient, and stable under Courant–Friedrichs–Lewy criterion (0<τ≤0.25; τ is the iteration step) [20].

Now, let us define gradients in the four directions of the scheme—North, South, East, and West—respectively as Δi,jN=ui,j+1−ui,j, Δi,jS=ui,j−1−ui,j, Δi

Results

Visual results show that when images are heavily corrupted by noise, most old edge detectors—particularly Canny, LoG, TV, and PM—generate false and/or weaker edges. Our method, however, produces well-defined and stronger edges and efficiently suppresses unwanted artifacts (Fig. 4, Fig. 5, Fig. 6). These observations can be objectively quantified in Table 1, Table 2, where our method yields higher quality values.

Discussions

We quantified our results using an edge-similarity-metric (ESIM) in [23], [24], which addresses potential weaknesses of traditional quality metrics (which is that they fail to measure the strength and quality of edges). The ESIM is defined byESIM=PSNR˜(EM(u),EM(uo)), where EM(u) and EM(uo) are, respectively, the edge maps of u (processed image) and uo (original image), andPSNR˜=10log10⁡PQ|max⁡(uo)−min⁡(uo)|2‖u−uo‖22 is as defined in [24]; P and Q are horizontal and vertical runs of either u or u

Conclusion

This paper has proposed a diffusion-driven iterative method to extract edges from noisy images. Both qualitative and quantitative results demonstrate the effectiveness of the method to generate stronger and clearer edges. As the new approach is robust against noise, it can benefit most computer vision tasks for real world scenes.

The next phase of the research is to use the proposed diffusion equation in (2) as a regularizer to address the ill-posedness of some inverse problems. In particular,

Acknowledgement

The authors of this manuscript declare that none of the organizations funded the research.

References (25)

  • P. Perona et al.

    Scale-space and edge detection using anisotropic diffusion

    IEEE Trans. Pattern Anal. Mach. Intell.

    (1990)
  • S. Kichenassamy

    The Perona–Malik paradox

    SIAM J. Appl. Math.

    (1997)

    • Cited by (10)

    • Robust edge detection based on Modified Moore-Neighbor

      2018, Optik
      Citation Excerpt :

      Figs. 11(e) and 12(e) signify the output images using the proposed method for the input images BSD135069 and BSD41004 respectively. Furthermore Figs. 11(b) and 12(b) signify the output using the Moore neighborhood algorithm by Sharma et al. [12], Figs. 11(c) and 12(c) signify the output using the improved Sobel detector by Mathur et al. [11], and the outputs using active canny technique by Bastan et al. [24] are shown in Fig. 11(d) and 12(d). Using the proposed method, the detection of true edges of the object is clearly observed from the bare eye.

    • Anisotropic diffusion based denoising on X-radiography images to detect weld defects

      2017, Digital Signal Processing: A Review Journal
      Citation Excerpt :

      In order to remove noise without loss of fine details, a new variant of the flow is considered using weight parameter in the divergence diffusion process. Another category includes edge-preserving approaches that are based on changing the diffusion function or introducing new operations [15–23]. Barcelos et al. [15] approached the Well-Balanced Flow (WBF) based on Total Variation (TV), which is used in the divergence process of the P–M model.

    • Edge Detection Scheme Based on the Multi-Resolution form of Singular Value Decomposition

      2023, International Conference on Electrical, Computer and Energy Technologies, ICECET 2023

    • A Nonlinear Diffusion Model with Smoothed Background Estimation to Enhance Degraded Images for Defect Detection

      2023, Applied Sciences (Switzerland)

    • On the convexification of the Perona–Malik diffusion model

      2020, Signal, Image and Video Processing

    • Edge and region segmentation in high-resolution aerial images using improved kernel density estimation: A hybrid approach

      2020, Journal of Intelligent and Fuzzy Systems
    View all citing articles on Scopus
    View full text
    Copyright © 2015 Elsevier B.V. All rights reserved.