The Synergy Between Different Colour Spaces For Degraded Colour Images Segmentation

Image segmentation is a fundamental and challenging task in many subjects such as image processing and computer vision. Even though image segmentation seems obvious to a human observer, the problem is still very difficult to solve by a computer. Lots of work focus on segmenting natural colour images; however, when the given images are corrupted by different types of degradations – like noise, information loss and/or blur – the segmentation problem can be more challenging.

As to degraded colour images segmentation, can we still do a comparable segmentation work compared to the state-of-the-art achievements which are focusing on non-degraded ones? If so, can we keep the proposed method as simple as possible, at least not involving more computational overhead? With these basic concerns and our understanding of image segmentation and different colour spaces, we bring our solution, a method called SLaT – Smoothing, Lifting, and Thresholding.

The key point of the method SLaT is the lifting step, which is manipulating the synergy between different colour spaces e.g. RGB, HSI, CB, Lab, etc. This synergy will provide us rich information for the subsequent segmentation, as well as ensuring that even if the first colour space has highly correlated channels, we can still have enough information to obtain good segmentation results. The SLaT method can be described as the following three stages.

Figure 1: Segmentation results of the proposed SLaT method. (a) Noisy image; (b) Result without the synergy between colour spaces at Stage two; (c) Result with the synergy between colour spaces. The original test image can be found at jects/CS/vision/bsds/. Source: https://www2.eecs.berkeley.edu/Research/Projects/CS/vision/bsds/

– Stage one. Let the given degraded image be in space V1. A convex variational model is first applied in parallel to each channel of V1. This then yields a unique restored smooth image.

– Stage two. The second stage, which consists of colour dimension lifting, is the synergy between different colour spaces. Firstly, the smooth colour image obtained at Stage one is transformed to a secondary colour space V2 that provides us with complementary information; then these images are combined as a new vector-valued image composed of all the channels from colour spaces V1 and V2.

– Stage three. A multichannel thresholding is finally applied to the combined V1-V2 image to obtain a segmented image with K phases. Here K is a preset number of phases. Different values of K will lead to segmentation results with different phases. Note, however, that tuning K does not influence the previous two stages but the last Stage three which can be solved very fast.

Without loss of generality, V1 is fixed to be the RGB colour space since one usually has RGB colour images. The Lab colour space is used as the secondary colour space V2 since it is often recommended for colour segmentation. Figure 1 shows the results of the SLaT method, clearly, without the help of the synergy of different colour spaces, a disappointing result is obtained (see Figure 1 (b)); fortunately, this disappointment is easy to be cleared up after involving the synergy between different colour spaces (see Figure 1 (c)).

In sum, the new three-stage method, named SLaT for Smoothing, Lifting, and Thresholding, has the ability to segment images corrupted by e.g. noise, blur, or when some pixel information is lost. Experimental results on an RGB image coupled with Lab secondary colour space demonstrate that method SLaT has great performance both in terms of quality and computational time for images corrupted by noise. Now, why not try more tests using method SLaT on your own images at hand with other degradations like information loss and/or blur?

These findings are described in the article entitled A Three-Stage Approach for Segmenting Degraded Color Images: Smoothing, Lifting and Thresholding (SLaT), recently published in the Journal of Scientific Computing. This work was led by Xiaohao Cai (University of Cambridge), Raymond Chan (The Chinese University of Hong Kong), Mila Nikolova (Université Paris-Saclay) & Tieyong Zeng (Hong Kong Baptist University).

About The Author

Xiaohao Cai

Xiaohao is a research scientist at the University of Cambridge.

In particular, I am interested in:

  • Image segmentation and object tracking
  • Image registration; Wavelets
  • Compressed sensing
  • Applications in processing of digital image, video, biomedical imaging (MRI, CT, kVCT, MVCT), remote sensing data, just to name a few
Raymond Chan

Raymond Chan graduated with First Class Honors from the Department of Mathematics at The Chinese University of Hong Kong in 1980. Uncertain of what to do next, he stayed in the Department as a full-time instructor after graduation. He started his graduate study in 1981 with a full fellowship from the Courant Institute of Mathematical Sciences at New York University. He obtained the M.Sc. and Ph.D. degrees in Applied Mathematics there in 1984 and 1985 respectively under the supervision of Professor Olof Widlund.

Chan began his career as a tenure-track Assistant Professor at the University of Massachusetts at Amherst in 1985. With heart and mind always in Hong Kong, he came back to Hong Kong in 1986, first at The University of Hong Kong (1986-92) and then at The Hong Kong University of Science and Technology (1993) before joining his Alma Mater in 1993. He was the Associate Director of the Institute of Mathematical Sciences (1996-98), the Associate Dean of Science (2004-2009) and the Head of the Mathematics Department (2012-2018). He has retired from the University in 2019 as an Emeritus Professor. He is now the Dean of College of Science at City University of Hong Kong.

Chan has published 140 journal papers and has been in the ISI Science Citation List of Top Highly-Cited Mathematicians in the world (2001 List). He won a Leslie Fox Prize for Numerical Analysis in 1989 at Cambridge, United Kingdom; a Feng Kang Prize of Scientific Computing in 1997 in Beijing, China; a Morningside Award in 1998 in Beijing, China; and 2011 Higher Education Outstanding Scientific Research Output Awards (First Prize) from the Ministry of Education in China. He was elected a SIAM Fellow in 2013 and a SIAM Council Member for 2015-20.

Chan has served on the editorial boards of many journals, including: Asian Journal of Mathematics (co-Chief Editor since 1997), Advances in Computational Mathematics (since 2010), Journal of Mathematical Imaging and Vision (since 2014), Journal of Scientific Computing (since 2013), SIAM Journal on Imaging Sciences (from 2007 to 2017), and SIAM Journal on Scientific Computing (from 2000 to 2008). He presented over 170 invited conference talks in more than 20 countries, including plenary talks at SIAM Conference on Applied Linear Algebra and SIAM Conference on Imaging Science. He also reviewed papers for more than 120 different journals.

MN
Mila Nikolova

Mila is a research scientist at the Université Paris-Saclay.

Tieyong Zeng

Tieyong is a research scientist at the Hong Kong Baptist University.

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