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Real-time saliency detection for greyscale and colour images

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Abstract

Unsupervised salient image generation without the aid of prior assumptions has many applications in computer vision. We present three unique real-time saliency generation algorithms that provide state-of-the-art performance for greyscale and colour images. Our fastest method run under 50 ms per frame on average. Our algorithm introduces a novel weighted histogram of orientation feature to supplement image intensity for monochromatic image manifold ranking. We also provide a method of dimensional reduction for the non-normalized optimal affinity matrix (OAM) using principal components analysis; this novel technique allows faster computation and stabilization of the OAM inversion process. We compare our methods with 18 traditional and recent techniques using three standard and custom datasets including ECSSD, DUT-OMRON and MSRA10K totalling 32,536 images for colour and greyscale variations. The results show our method to be more than \(10{\times }\) faster than the RC and GMR models and having similar or better precision performances.

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Notes

  1. https://mmcheng.net/salobjbenchmark/.

  2. Discounting the discontinuous subpixels.

  3. http://ai-automata.ca/research/hisafe.html.

  4. AMD FX-8350 8-4.0GHz.

  5. AMD A4-5000-APU 4-1.5GHz.

  6. Intel 2-Quad-Q6600 4-2.4GHz.

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Acknowledgements

The first author wishes to thank Dr. Gerhard Roth of Carleton University for his continuing guidance and support.

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  1. Mechanical and Aerospace Engineering Department, Carleton University, Ottawa, Canada

    Jian-Feng Shi & Steve Ulrich

  2. MDA Neptec Design Group Ltd., Ottawa, Canada

    Stéphane Ruel

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This research was jointly funded by the NSERC Scholarship CGSD3-453738-2014, CSA STDP and OCE VIP II Award 24053.

Proofs

Proofs

The proof of Lemma 1 is as follows,

Proof

If the alternative form of \(\bar{\mathbf {A}}\) from Lemma 1 is equivalent, then when multiplied by the inverse it will result in the identity.

$$\begin{aligned} \begin{aligned}&\left( \mathbf {1}-\alpha \mathbf {E}\mathbf {F}\right) \left( \mathbf {1}-\mathbf {E} \left( \mathbf {F}\mathbf {E}-\frac{1}{\alpha }\mathbf {1}_{d}\right) ^{-1} \mathbf {F}\right) \\&\quad = \mathbf {1} -\alpha \mathbf {E}\mathbf {F} -\mathbf {E}\left( \mathbf {F}\mathbf {E}-\frac{1}{\alpha }\mathbf {1}_{d}\right) ^{-1}\mathbf {F} +\alpha \mathbf {E}\mathbf {F}\mathbf {E}\left( \mathbf {F}\mathbf {E} -\frac{1}{\alpha }\mathbf {1}_{d}\right) ^{-1}\mathbf {F} \\&\quad = \mathbf {1} -\alpha \mathbf {E}\mathbf {F} +\alpha \mathbf {E}\left( -\frac{1}{\alpha }\mathbf {1}_{d}+\mathbf {F}\mathbf {E}\right) \left( \mathbf {F}\mathbf {E}-\frac{1}{\alpha }\mathbf {1}_{d}\right) ^{-1}\mathbf {F} \\&\quad = \mathbf {1} \end{aligned} \end{aligned}$$

\(\square \)

The proof of Corollary 1 is as follows,

Proof

Substituting Lemma 1 into Eq. (6), and using the previous definitions for \(\mathbf {E}\) and \(\mathbf {F}\),

$$\begin{aligned} \begin{aligned} \mathbf {A}&=\left( \mathbf {D}-\alpha \mathbf {W}\right) ^{-1} \\&=\mathbf {D}^{-\frac{1}{2}}\left( \mathbf {1}-\mathbf {E}\left( \mathbf {F}\mathbf {E} -\frac{1}{\alpha }\mathbf {1}_{d}\right) ^{-1}\mathbf {F} \right) \mathbf {D}^{-\frac{1}{2}} \\&=\mathbf {D}^{-1} \left( \mathbf {1}-\mathbf {P}\left( \mathbf {Q}\mathbf {D}^{-1}\mathbf {P} -\frac{1}{\alpha }\mathbf {1}_{d}\right) ^{-1}\mathbf {Q}\mathbf {D}^{-1}\right) \end{aligned} \end{aligned}$$

\(\square \)

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Shi, JF., Ulrich, S. & Ruel, S. Real-time saliency detection for greyscale and colour images. Vis Comput 37, 1277–1296 (2021). https://doi.org/10.1007/s00371-020-01865-x

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