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SOME REMARKS ON THURSTON METRIC AND HYPERBOLIC METRIC
Sun, Zongliang Korean Mathematical Society 2016 대한수학회보 Vol.53 No.2
In this paper, we study the relations between the Thurston metric and the hyperbolic metric on a closed surface of genus $g{\geq}2$. We show a rigidity result which says if there is an inequality between the marked length spectra of these two metrics, then they are isotopic. We obtain some inequalities on length comparisons between these metrics. Besides, we show certain distance distortions under conformal graftings, with respect to the $Teichm{\ddot{u}}ller$ metric, the length spectrum metric and Thurston's asymmetric metrics.
Some remarks on Thurston metric and hyperbolic metric
Zongliang Sun 대한수학회 2016 대한수학회보 Vol.53 No.2
In this paper, we study the relations between the Thurston metric and the hyperbolic metric on a closed surface of genus $g \geq 2.$ We show a rigidity result which says if there is an inequality between the marked length spectra of these two metrics, then they are isotopic. We obtain some inequalities on length comparisons between these metrics. Besides, we show certain distance distortions under conformal graftings, with respect to the Teichm\"uller metric, the length spectrum metric and Thurston's asymmetric metrics.
No-reference Image Blur Assessment Based on Multi-scale Spatial Local Features
( Chenchen Sun ),( Ziguan Cui ),( Zongliang Gan ),( Feng Liu ) 한국인터넷정보학회 2020 KSII Transactions on Internet and Information Syst Vol.14 No.10
Blur is an important type of image distortion. How to evaluate the quality of blurred image accurately and efficiently is a research hotspot in the field of image processing in recent years. Inspired by the multi-scale perceptual characteristics of the human visual system (HVS), this paper presents a no-reference image blur/sharpness assessment method based on multi-scale local features in the spatial domain. First, considering various content has different sensitivity to blur distortion, the image is divided into smooth, edge, and texture regions in blocks. Then, the Gaussian scale space of the image is constructed, and the categorized contrast features between the original image and the Gaussian scale space images are calculated to express the blur degree of different image contents. To simulate the impact of viewing distance on blur distortion, the distribution characteristics of local maximum gradient of multi-resolution images were also calculated in the spatial domain. Finally, the image blur assessment model is obtained by fusing all features and learning the mapping from features to quality scores by support vector regression (SVR). Performance of the proposed method is evaluated on four synthetically blurred databases and one real blurred database. The experimental results demonstrate that our method can produce quality scores more consistent with subjective evaluations than other methods, especially for real burred images.