Color Edge Detection based on Bhattacharyya Distance

Yongsung Cheon and Chulhee Lee

Dept. of Electrical and Electronics Engineering, Yonsei University, Republic of Korea

Keywords: Bhattacharyya Distance, Colour Edge Detection, Multi-dimensional Edge Detection.

Abstract: In this paper, we propose to apply the multi-dimensional edge detection algorithm developed for hyperspectral

images to colour image edge detection. The multi-dimensional edge detection algorithm utilizes the

Bhattacharyya distance and considers the statistical difference between two neighbouring blocks. In order to

apply the algorithm to colour images, we need to take into account the singularity problem of the covariance

matrices. In the algorithm, we first apply the Wiener filter to supress noise and select four block pairs

including up-down, left-right, diagonal-left-down and diagonal-right-down. The experimental results show

that the colour edge detection method based on the Bhattacharyya distance shows promising results compared

to the results obtained by the Sobel and Canny-edge edge detection algorithms.

1 INTRODUCTION

Edge detection is a basic operation in pattern recogni-

tion and image processing. Although many researchers

have proposed numerous algorithms, edge detection is

still a challenging problem. Due to the complexity of

typical images, current edge detection algorithms fail

to produce satisfactory edges in some cases. Most

images are available in colour. In general, colour image

edge detection should provide better performance

compared to grey scale images, though the difference

may not be significant in some cases. Among various

edge detection algorithms, the Sobel and Canny edge

detection algorithms are still widely used.

Recently, the Bhattacharyya distance was used to

detect edges in multispectral images. By utilizing

second order statistics, it can better utilize the

information of multispectral images. In this paper, we

explore the edge detection algorithm based on the

Bhattacharyya distance for colour image edge

detection.

The rest of this paper is organized as follows: Section

2 summarizes the edge detection algorithm based on

the Bhattacharyya distance along with some

modifications to solve the singularity problem of

colour images. Section 3 presents experimental results

and conclusions are provided in section 4.

2 THE METHOD

Fig. 1 is a block diagram of edge detection using the

Bhattacharyya Distance. We used several colour

images to test the performance. First, we apply the

Wiener filter to RGB images to supress noise. Then,

four block pairs are selected and the Bhattacharyya

distances of the four pairs are computed. Finally, the

maximum value is selected as an edge value.

2.1 Pixel-wise Wiener Filter

Most images often contain artefacts that may

adversely affect edge detection. To avoid this

problem, a pixel-wise adaptive Wiener filter based on

statistical characteristic estimation from the local

neighbourhood of each pixel was used.

The Wiener filter is commonly used in image

processing applications to remove additive noise

from degraded images. The local mean ( μ ) and

variance (



) are computed as follows:

()





(1)

368

Cheon, Y. and Lee, C.

Color Edge Detection based on Bhattacharyya Distance.

DOI: 10.5220/0006433903680371

In Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2017) - Volume 2, pages 368-371

ISBN: Not Available

Figure 1: Block diagram of the proposed method.

()

222

Lij

=−





(2)

where L(i,j) represents a block image in the N-by-M

local neighbourhood of each pixel. Then, the Wiener

filter is given as follows:

()

[]

,(,).Wij Lij

συ

μμ

−

=+ −

(3)

2.2 Bhattacharyya Distance

For each pixel, four pairs of blocks were chosen: up-

down, left-right, diagonal-left-down and diagonal-

right-down pairs. Fig. 2 illustrates the four pairs of

blocks.

The Bhattacharyya distance takes into account the

mean and covariance differences. Therefore, it can

better utilize multispectral images, including colour

images. The Bhattacharyya distance can be defined as

follows:

()()

12 12

11det

det det

μμ μμ



=− −+







ΣΣ

   

(4)

where 







and ∑



are the mean vector and covariance

matrix of the 



block, and ∑=

∑



∑





The up-down blocks are used to find vertical edges

whereas the left-right blocks are used to find

horizontal edges. The diagonal-left-down blocks and

diagonal-right-down blocks are used to detect

diagonal edges. We compute four Bhattacharyya

distances and choose the maximum value, which

represents the edge strength as follows:

() () () () ()

()

,, , .

dgeimage i Max UD i LR i DLD i DRD i=

(5)

Figure 2: Four pairs of neighbourhood blocks. (a) Up-down

(UD), (b) Left-right (LR), (c) Diagonal-left-down, (d)

Diagonal-right-down.

2.3 Outliers and Singularity Problem

There is a possibility that a block may contain outlier

pixels, which cause a large variance. Such outlier

pixels may generate erroneous edge pixels. To

address this problem, outliers are removed before

computing the mean vector and covariance matrix.

Unlike multi-spectral images, a small block can be

very homogeneous in colour images. It is also

possible that a block may have the same RGB values

if it represents constant regions. In such cases, the

covariance matrix is singular and the Bhattacharyya

distance cannot be computed since the determinant is

zero. To solve this problem, we add a very small value

(ε) to the diagonal terms of the covariance matrix.

Table. 1 illustrates this procedure.

Table 1: Covariance Matrix.





+ 















+ 















+

Color Edge Detection based on Bhattacharyya Distance

369

3 EXPERIMENTAL RESULTS

In the experiments, we set the block size to 3x3 pixels

and the offset to one pixel to compute the

Bhattacharyya distance. Along with the colour edge

detection method based on the Bhattacharyya

distance (BD method), we tested the Sobel and Canny

edge detection algorithms.

Figs. 3-6 show performance comparisons of the three

methods. In Fig. 3, the Sobel and Canny edge

detection algorithms failed to detect the weak edges

between the top of the box and the white wall,

whereas the BD method successfully recovered the

edges. In Fig. 4, the Sobel and Canny edge detection

algorithms failed to detect the boundary between the

wheel and the shadow background, whereas the BD

method better recovered the missing edges. In Fig. 6,

the Sobel and Canny edge detection algorithms

completely failed to detect the dark building, whereas

the BD method detected the building structure.

4 CONCLUSIONS

In this paper, we applied the edge detection algorithm

based on the Bhattacharyya distance for colour image

edge detection. In order to solve the covariance

singularity problem, we added a very small value to

the diagonal terms of the covariance matrix.

Experimental results show that the edge detection

algorithm based on the Bhattacharyya distance can

detect some edges missed by the Sobel and Canny-

edge detection algorithms.

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(a) (b) (c) (d)

Figure 3: Performance comparison. (a) Original image, (b) Sobel filtering, (c) Canny edge detection, (d) the colour edge

detection based on the Bhattacharyya Distance.

ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics

370

(a) (b) (c) (d)

Figure 4: Performance comparison. (a) Original image, (b) Sobel filtering, (c) Canny edge detection, (d) the colour edge

detection based on the Bhattacharyya Distance.

(a) (b) (c) (d)

Figure 5: Performance comparison. (a) Original image, (b) Sobel filtering, (c) Canny edge detection, (d) the colour edge

detection based on the Bhattacharyya Distance.

(a) (b) (c) (d)

Figure 6: Performance comparison. (a) Original image, (b) Sobel filtering, (c) Canny edge detection, (d) the colour edge

detection based on the Bhattacharyya Distance.

Color Edge Detection based on Bhattacharyya Distance

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