Area operators for edge detection

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Abstract

In area morphology, the area open–close (AOC) and close–open (ACO) operations are based on filtering the connected components in the image level sets. Unlike traditional morphology that enforces the shape of the structuring element on image region boundaries, area morphology allows removal of small features without boundary distortion. This study defines ascending and descending objects that depend on the area of the connected components of the level sets. The major contribution of the paper is to define image edges at the boundaries of the ascending and descending objects. From this area morphology approach, thin, closed contours are provided that are suitable for use in image segmentation. A notable strength of the area morphology edge detector is that it does not require the use of a threshold. The edge maps are Euclidean invariant and causal, and yield good performance in terms of edge localization and the suppression of below-scale detail. The results demonstrate the superior performance of the area operator-based edge detection over the conventional techniques.

Introduction

Estimation of an edge map of a scene is a well-researched topic in pattern recognition and related fields. Various edge detection schemes have been developed that provide moderate to good result in segmenting images (Jain et al., 1995). In this initiative, we explore the application of area morphology to the problem of edge detection. To date, the area morphology operators have been utilized primarily in image filtering, enhancement and reconstruction (Salembier and Serra, 1995).

Area operators are based on the properties of connected components within the image level sets. In the present application, we have utilized the area property of the connected components (essentially the number of pixels in a particular connected component). The major advantage of area morphology, which is revealed in the edge detection results, is that, unlike standard morphology, area morphology does not impose the shape of a structuring element on the constituent image regions.

At the onset, we define the terms used in the proposed edge detection technique. It is well known that a perceptually relevant edge map is a function of image scale (Marr, 1982). For the present approach, we would also like to detect edges at predefined image scales such that unnecessary image details irrelevant for semantic interpretation could be excluded from the final result. However, in other scale-sensitive edge filters, this is achieved at the cost of edge localization error and distortion in the edge map Marr and Hildreth, 1980, Torre and Poggio, 1986. Other edge detectors produce undesirable artifacts such as fragmented edge segments or thick edges that require expensive and heuristic post-processing.

In contrast, area-based edge operators do not produce edge localization error or edge distortion. The connected invariant area operators remove or preserve connected components in their entirety. In this way, regions are not distorted in part. The preservation of a given feature depends on feature area only. The area operators not only provide a scaling for edge detection but also eliminate spurious regions due to noise.

Here, connected invariant operators are introduced that provide a multi-scale image representation. Within the image representation, ascending and descending objects are defined. Edges are extracted by locating the boundary between ascending and descending object pixels in the processed imagery. We have shown that desirable properties such as Euclidean invariance and causality, relevant for any edge detection scheme, are maintained for the proposed method. Other important aspects of the proposed algorithm include edge contiguity, edge thinness, and independence from thresholds.

The paper is organized as follows. First, definitions and operators necessary for description of the edge detection method are provided in Section 2. This discussion is followed by the description of the edge detection technique in Section 3. Results for a number of images and comparison with results of other multi-scale edge detection schemes are provided in Section 3, with conclusions in Section 5.

Section snippets

Definitions

We start with the definition of image level sets and the associated connected components. These definitions are followed by the specification of the area morphology operators.

Definition 1

For a discrete domain image I ⊂ Z2 and image location p, level set s at l, l∈[0,L], is defined bys(p)=1∀p:I(p)⩾l,0otherwise.Therefore, the level set is a binary image representation of the image at a specified intensity level.

Definition 2

For a level set s (at level l) and an image location p, the connected component Cs(p) at p is

Edge detection

Ideally, we seek the potential edge points that represent boundaries between image objects. However, the term object itself is not defined. To tackle this problem, we introduce two types of objects that are defined by connected components within the image level sets.

Definition 5

The connected components that represent ascending objects, C∪(p), and descending objects, C∩(p), are defined as follows. For an area-scaled image Ira, the potential ascending object at image location p is given by C∪(p)={q:∃PI⩾l

Results

Edge detection results using area operators and comparisons to traditional edge operators are presented in this section. Note that the primary objective of the proposed edge detector is to detect edges relevant for pattern recognition. Appropriate scales are selected to detect meaningful object boundaries for which post-processing is not required, providing semantic interpretation of object shapes. Therefore, unnecessary image details and noise should be removed in the scaling/filtering process.

Conclusions

We have shown that the proposed edge detection technique can detect edges sufficient for semantic interpretations without post-processing such as edge-linking or edge-filtering. The approach is based on a scale-sensitive filtering process that leads to edge maps of the prescribed scale. Note that the entire process is devoid of any threshold selection, in contrast to traditional edge detection techniques. The area morphology edge detection method is currently being used in two multi-media

References (8)

  • J. Canny

    A computational approach to edge detection

    IEEE Trans. PAMI

    (1986)
  • R. Deriche

    Using Canny's criteria to derive a recursively implemented optimal edge detector

    Internat. J. Comput. Vision

    (1987)
  • R. Jain et al.

    Machine Vision

    (1995)
  • D. Marr

    Vision

    (1982)
There are more references available in the full text version of this article.

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1

D.P. Mukherjee was visiting the Oklahoma Imaging Laboratory, Oklahoma State University, USA, from Electronics and Communication Sciences Unit, Indian Statistical Institute, India 700035.

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