ε > 0 and S0 represents the initial saturation component. This is a simple extension from the mean curvature flow by projecting the mean curvature flow to the normal direction and rescaling the intensity component I to kI. Basically this flow smoothes an image in the direction parallel to the edges. The positive constant k is used to amplify image edges, and the anisotropic diffusion becomes the isotropic heat equation when k = 0. The interested reader is referred to [15] for more details and illustrations of this modified curvature flow.

4. EXPERIMENTS

Two sets of color photos have been collected by a Canon 350D and 400D on the same indoor scenes with different ISO settings. The low and high ISO photos of one scene are used as the ground truth and the noise corrupted version. The photos are obtained with a carefully calibrated indoor setup to maintain the consistence of lighting between two photo captures. The photo scene contains only static objects to avoid any motion blur. Only shutter speed is adjusted to maintain the same exposure. Aperture is kept fixed to preserve the same depth of field in both low and high ISO photos. As introduced in Introduction, with the ground truth available, we can conduct a comprehensive performance comparison between our algorithm and 14 recognized approaches for different color spaces (CB [11,21], HSV [21,22] and RGB spaces [4,5,6,7,8,13,15,16,24,25]), and 2 commercial color photo denoising software (NoisewareTM [62] and PhotoshopTM), using both quantitative (PSNR and MSE) and qualitative (visual perception) measures. Here we present four approaches with the highest ranked performance from the quantitative comparison, i.e., the modified curvature flow [15], vector diffusion [6], non-local mean algorithm [25] and CB TV [13], as well as a photo denoising software (NoisewareTM).

Figure 5(a) illustrates a low ISO photo (ISO=100, size=500×500) as the ground truth. Figure 5(b) and 5(c) are the corresponding high ISO (ISO=1600) noisy photo and our GVFbased approach denoising result. In order to clearly view the performance of the selected approaches on different image features (e.g. edge, smooth region, slope and texture), we only display four enlarged regions (see Figure 5(a)) in the high and low ISO photos (Figure 5(d) and 5(e)) and the denoising results. The results of Figure 5(f)-(k) are sorted by the optimal PSNR and MSE values for visual comparison. Due to the close PSNR (MSE) values, these results look similar on the whole. Though, as the error increases, it can be seen some small features are smoothed away from the truth (e.g. at the left region 4). To test more varied images, we repeated this comparison on other four image pairs. Figure 8 illustrates the quantitative comparison of our approach with others by sorting the mean PSNR and MSE values. With these error measures, the GVF-based approach outperforms the other approaches in average.

The low and high ISO images were cut separately from big pictures (3456×2304 or 3888×2592) taken at the same scene with different ISO settings.

above the bars are the corresponding mean values of the PSNR and MSE. The standard deviation values are marked as the vertical lines on the bars. It can be seen the proposed approach outperforms other methods with the quantitative measures in average.

Figure 9. Error chart sorted by the average of PSNR (MSE).

In our experiments, the algorithm parameters were fine-tuned for the “best” results by a multi-scale coarse-to-fine scheme. Specifically, the data fidelity terms in the HSI diffusion equations (Eqs. (12), (21) and (22)) guarantee a convergent diffusion process. With all parameters being fixed except the iteration number, an example of the MSE convergence is shown in Figure 10(a), from which it can be seen that the diffusion process converges after about 1000 iterations. For the HSI diffusion algorithm, the iteration number was selected as 2000 for the optima. The GVF parameters are also fixed in our experiments with μ=0.2 and an iteration number 80 to compute the GVF fields for all images. Given a high ISO photo, the initial parameter settings are obtained by manually selecting the parameters, based on experience, and iterating the process until a quantitatively acceptable result was obtained (e.g. with the improved MSE and PSNR measures). Then we adjust the initial value for each parameter by both increasing and decreasing it until the result error measures become worse (e.g. an increase of the MSE), and the turning point is considered as the approximate optimum§. The steps to determine the approximate optimum proceed in a multi-scale fashion. For each parameter, we start with a coarse resolution consisting of large “jump” between step values to determine the approximate optimum, while other parameters are fixed with their initial or optimal values. Based on the approximate optimum, a variation range is selected for

The parameter tuning was implemented in a semi-automatic way, i.e., a variation range for each parameter was manually selected at first, then a multi-scale searching scheme with different step values was applied to locate the optimum, or suboptimum results. The true optimum is determined by several factors, including the parameter resolution and dependency on each other. In our experiments, we record the intermediate results every 10 iterations in the diffusion process, and the step values (resolution) to update each parameter is changed dynamically as described in Footnote 5. Moreover, we assume that parameters are independent with each other, as described later in this paragraph.

§In fact only one turning point will be located in either increasing or decreasing direction due to the convergent process, i.e., the parameter curves are all unimodal, see Figure 10(b).