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摘要: 针对目前彩色图像灰度化难以充分保留原彩色图像对比度的问题，本文提出了基于最大加权投影求解的彩色图像灰度化模型及算法.首先，在好的彩色图像灰度化算法应使灰度化图像具有最大对比度的假设下，本模型提出最大加权投影的目标优化函数，并且将原始彩色图像梯度权重引入到最大化函数中，使得原彩色图像中对比度较小的区域也能够在灰度化后的图像中得到保持.每个彩色通道梯度的高斯加权系数反映灰度图像的对比度和原彩色图像的颜色顺序.其次，对所提模型使用参数离散搜索策略求解，通过对线性离散参数模型产生的候选图像进行搜索，由于只有几个算术运算，计算速度较快.最后，为评价所提出算法在复杂场景下图像灰度化对比度保持性能，本文对Cadik、CSDD和COLOR250数据集分别进行灰度化实验.定性和定量实验结果表明，所提算法相比于其他算法能较好地保留原彩色图像颜色对比度，同时具有对噪声鲁棒和运算速度快的优势.Abstract: This paper presents a color-to-gray conversion model for faithfully preserving the contrast details of the original color image. First, on the basic assumption that a good gray conversion should make the conveyed gradient values to be maximal, we present a maximum weighted projection function to model the decolorization procedure, incorporating weights of the original gradients into the maximization problem. The Gaussian weighted factor consisting of the gradients of indivisual channels of the input color image is employed to better reflect the degree of preserving feature discriminability and color ordering. Second, a discrete searching solver is proposed by determining the solution with the loss function value from the linear parametric model-induced candidate images. The non-iterative solver has advantages in simplicity and speed with only several simple arithmetic operations, leading to real-time computational speed. Finally, extensive experimental evaluations on the existing datasets show that the proposed method outperforms the state-of-the-art methods quantitatively and qualitatively.
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图 3 Cadik数据集彩色图像灰度化转化结果
((a)输入彩色图像; (b) Gooch算法; (c) rgb2gray算法; (d) CP算法; (e) RTCP算法; (f) MWPDe算法)
Fig. 3 Color-to-gray conversion results of Cadik dataset
((a) Input images; (b) Gooch; (c) rgb2gray; (d) CP; (e) RTCP; (f) MWPDe)
图 4 CSDD数据集彩色图像灰度化转化结果
((a)输入彩色图像; (b) Gooch算法; (c) rgb2gray算法; (d) CP算法; (e) RTCP算法; (f) MWPDe算法)
Fig. 4 Color-to-gray conversion results of CSDD dataset
((a) Input images; (b) Gooch; (c) rgb2gray; (d) CP; \\(e) RTCP; (f) MWPDe)
图 5 COLOR250数据集彩色图像灰度化转化结果
((a)输入彩色图像; (b) Gooch算法; (c) rgb2gray算法; (d) CP算法; (e) RTCP算法; (f) MWPDe算法)
Fig. 5 Color-to-gray conversion results of COLOR250 dataset
((a) Input images; (b) Gooch; (c) rgb2gray; \\(d) CP; (e) RTCP; (f) MWPDe)
图 8 噪声方差为0.03时对Cadik数据集进行抗噪性能分析
((a)输入彩色图像; (b) rgb2gray算法; (c) CP算法; (d) RTCP算法; (e) MWPDe算法)
Fig. 8 Antinoise performance analysis of Cadik dataset with 0.03 noise variance
((a) Input images; (b) rgb2gray; (c) CP; (d) RTCP; (e) MWPDe)
图 9 算法对低分辨率图像实验效果
((a)输入低分辨率彩色图像(下采样2个因子); (b) rgb2gray算法; (c) CP算法; (d) RTCP算法; (e) MWPDe算法)
Fig. 9 Experiment results on the low resolution images
((a) Input low resolution color images (2 downsampling factor); (b) rgb2gray; (c) CP; (d) RTCP; (e) MWPDe)
图 10 参数敏感度分析
((a)相似系数 ${{S}_{x, y}}(t)$ 随 $t$ 的变化趋势; (b)输入彩色图像; (c) $t=0.01$ 时WMPDe算法灰度化效果; (d) $t=0.00001$ 时WMPDe算法灰度化效果)
Fig. 10 Sensitivity study of parameters
((a) Similar coefficients variation tendency ${{S}_{x, y}}(t)$ with $t$ ; (b) Input color images; (c) $t=0.01$ ; (d) $t=0.00001$ )
表 1 Cadik数据集的CCPR值
Table 1 CCPR value of Cadik dataset
τ Gooch rgb2gray CP RTCP MWPDe 1 0.96 0.93 0.97 0.96 0.96 2 0.93 0.88 0.94 0.94 0.94 3 0.91 0.84 0.92 0.92 0.92 4 0.89 0.8 0.91 0.9 0.91 5 0.87 0.77 0.89 0.89 0.9 6 0.85 0.75 0.87 0.87 0.88 7 0.83 0.73 0.86 0.86 0.87 8 0.81 0.71 0.84 0.85 0.86 9 0.79 0.69 0.83 0.83 0.85 10 0.77 0.68 0.82 0.82 0.84 11 0.75 0.66 0.8 0.8 0.84 12 0.72 0.65 0.79 0.79 0.83 13 0.7 0.63 0.77 0.77 0.82 14 0.69 0.62 0.76 0.76 0.81 15 0.67 0.61 0.75 0.75 0.81 
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表 2 CSDD数据集的CCPR值
Table 2 CCPR value of CSDD dataset
τ Gooch rgb2gray CP RTCP MWPDe 1 0.97 0.96 0.96 0.96 0.95 2 0.93 0.94 0.93 0.93 0.92 3 0.91 0.91 0.91 0.91 0.91 4 0.89 0.89 0.89 0.9 0.89 5 0.87 0.87 0.87 0.88 0.88 6 0.85 0.85 0.85 0.87 0.86 7 0.83 0.83 0.83 0.85 0.85 8 0.81 0.81 0.81 0.84 0.84 9 0.79 0.8 0.79 0.82 0.83 10 0.77 0.78 0.77 0.81 0.82 11 0.76 0.76 0.75 0.8 0.81 12 0.74 0.75 0.74 0.78 0.8 13 0.73 0.73 0.72 0.77 0.79 14 0.71 0.71 0.7 0.76 0.78 15 0.7 0.68 0.7 0.75 0.77
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表 3 COLOR250数据集的CCPR值
Table 3 CCPR value of COLOR250
τ Gooch rgb2gray CP RTCP MWPDe 1 0.95 0.96 0.96 0.96 0.95 2 0.92 0.93 0.93 0.93 0.92 3 0.89 0.9 0.9 0.9 0.9 4 0.86 0.87 0.88 0.88 0.88 5 0.83 0.85 0.86 0.86 0.86 6 0.81 0.83 0.84 0.84 0.85 7 0.79 0.81 0.82 0.83 0.83 8 0.76 0.79 0.8 0.81 0.82 9 0.74 0.77 0.79 0.8 0.81 10 0.72 0.75 0.77 0.78 0.8 11 0.7 0.74 0.76 0.77 0.79 12 0.68 0.72 0.74 0.76 0.78 13 0.67 0.7 0.73 0.75 0.77 14 0.65 0.69 0.72 0.74 0.76 15 0.63 0.67 0.7 0.72 0.75
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表 4 噪声情况下Cadik数据集的CCPR值
Table 4 CCPR value of Cadik dataset with noise added
τ rgb2gray CP RTCP MWPDe 1 0.92 0.95 0.94 0.96 2 0.86 0.91 0.91 0.92 3 0.82 0.87 0.88 0.89 4 0.78 0.84 0.85 0.86 5 0.74 0.82 0.84 0.84 6 0.72 0.79 0.82 0.82 7 0.7 0.77 0.81 0.81 8 0.68 0.75 0.8 0.79 9 0.66 0.73 0.78 0.78 10 0.65 0.71 0.77 0.77 11 0.63 0.7 0.76 0.76 12 0.62 0.68 0.75 0.75 13 0.61 0.66 0.74 0.74 14 0.6 0.65 0.73 0.74 15 0.58 0.64 0.72 0.73
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表 5 输入390×293彩色图像时不同算法的运行时间
Table 5 Runtime of different algorithms with the input 390×293 color image
Methods Gooch rgb2gray CP RTCP MWPDe Runtime (s) 3.00E+04 0.0048 0.5233 0.0728 0.0343
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