计算摄影学：高动态范围、超分辨率与图像合成

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"计算摄影学章节10涵盖了计算摄影的各种技术，包括光度校准、高动态范围成像、超分辨率与模糊去除、图像合成与遮罩、纹理分析与合成等核心概念。" 计算摄影学是计算机视觉领域的一个重要分支，它通过数学模型和算法来改进或扩展传统的摄影技术，实现更高级的图像处理效果。本章深入探讨了以下几个关键知识点： 1. 光度校准（Photometric Calibration）：这部分主要涉及相机的辐射响应函数，这是理解相机如何将光线转化为数字信号的关键。辐射响应函数描述了相机传感器对不同光强的敏感程度。此外，还包括噪声水平估计，这有助于理解并减少图像中的噪声。同时，还讨论了暗角（Vignetting）的影响以及光学模糊（Spatial Response）的估算，这些因素都会影响最终的图像质量。 2. 高动态范围成像（High Dynamic Range Imaging, HDR）：HDR技术用于捕捉和显示超过普通相机或显示器动态范围的图像。10.2.1节介绍了色调映射（Tone Mapping），这是一种将HDR图像压缩为可显示的低动态范围图像的技术。10.2.2节探讨了HDR在闪光摄影中的应用，通过结合多张曝光不同的照片，可以实现更好的光线平衡。 3. 超分辨率与模糊去除：10.3.1节讲述颜色图像去马赛克（Color Image Demosaicing），这是从单色滤镜阵列数据重建全彩色图像的过程。10.3.2节则介绍了颜色恢复（Colorization）的应用，能够将黑白图像或低色彩图像转化为全彩。这两个技术都能显著提高图像的细节和清晰度。 4. 图像遮罩与合成（Image Matting and Compositing）：这部分内容涵盖了多种遮罩技术，如蓝屏遮罩（Blue Screen Matting）、自然图像遮罩（Natural Image Matting）以及基于优化的遮罩（Optimization-based Matting）。这些技术常用于电影和特效制作，以精确地分离前景和背景。10.4.5节还提到了视频遮罩，适用于动态场景的合成。 5. 纹理分析与合成（Texture Analysis and Synthesis）：10.5.1节讲解了空洞填充和图像修复（Hole Filling and Inpainting）的技术，能有效地修复图像损坏部分。而10.5.2节则涉及非真实感渲染（Non-Photorealistic Rendering），这是一种使图像呈现出艺术风格的处理方法。 6. 额外阅读和练习：章节末尾提供了额外的阅读资料和习题，帮助读者深入理解和应用所学知识。计算摄影学不仅涵盖了理论基础，还包括了实际应用，是计算机视觉和图像处理领域中不可或缺的一部分。通过学习这些技术，专业人士可以创造出更加生动、真实的图像，并解决传统摄影无法处理的复杂视觉问题。

418 10 Computational photography

Figure 10.7 Calibration pattern with edges equally distributed at all orientations that can be used for PSF and

radial distortion estimation (Joshi, Szeliski, and Kriegman 2008)

 2008 IEEE. A portion of an actual sensed

image is shown in the middle and a close-up of the ideal pattern is on the right.

the sensed image. If desired, the pattern can be rendered at a higher resolution than the input

image, which enables the estimation of the PSF to sub-pixel resolution (Figure 10.8a). Finally

a large linear least squares system is solved to recover the unknown PSF kernel K,

K = arg min

B −D(I ∗ K)

, (10.1)

where B is the sensed (blurred) image, I is the predicted (sharp) image, and D is an optional

downsampling operator that matches the resolution of the ideal and sensed images (Joshi,

Szeliski, and Kriegman 2008). In terms of the notation (3.75) introduced in Section 3.4.3,

this could also be written as

b = arg min

o − D(s ∗ b)

, (10.2)

where o is the observed image, s is the sharp image, and b is the blur kernel.

If the process of estimating the PSF is done locally in overlapping patches of the image,

it can also be used to estimate the radial distortion and chromatic aberration induced by the

lens (Figure 10.8b). Because the homography mapping the ideal target to the sensed image

is estimated in the central (undistorted) part of the image, any (per-channel) shifts induced

by the optics manifest themselves as a displacement in the PSF centers.

Compensating

for these shifts eliminates both the achromatic radial distortion and the inter-channel shifts

that result in visible chromatic aberration. The color-dependent blurring caused by chromatic

aberration (Figure 2.21) can also be removed using the de-blurring techniques discussed in

Section 10.3. Figure 10.8b shows how the radial distortion and chromatic aberration manifest

themselves as elongated and displaced PSFs, along with the result of removing these effects

in a region of the calibration target.

The local 2D PSF estimation technique can also be used to estimate vignetting. Fig-

ure 10.8c shows how the mechanical vignetting manifests itself as clipping of the PSF in the

corners of the image. In order for the overall dimming associated with vignetting to be prop-

erly captured, the modiﬁed intensities of the ideal pattern need to be extrapolated from the

center, which is best done with a uniformly illuminated target.

This process confounds the distinction between geometric and photometric calibration. In principle, any ge-

ometric distortion could be modeled by spatially varying displaced PSFs. In practice, it is easier to fold any large

shifts into the geometric correction component.

10.2 High dynamic range imaging 419

−2 −1 0 1 2

−2

−1

−2 −1 0 1 2

−2

−1

−2 −1 0 1 2

−2

−1

−2 −1 0 1 2

−2

−1

(a)

(b) (c)

Figure 10.8 Point spread function estimation using a calibration target (Joshi, Szeliski, and Kriegman 2008)



2008 IEEE. (a) Sub-pixel PSFs at successively higher resolutions (note the interaction between the square sensing

area and the circular lens blur). (b) The radial distortion and chromatic aberration can also be estimated and

removed. (c) PSF for a mis-focused (blurred) lens showing some diffraction and vignetting effects in the corners.

When working with RAW Bayer-pattern images, the correct way to estimate the PSF is

to only evaluate the least squares terms in (10.1) at sensed pixel values, while interpolating

the ideal image to all values. For JPEG images, you should linearize your intensities ﬁrst,

e.g., remove the gamma and any other non-linearities in your estimated radiometric response

function.

What if you have an image that was taken with an uncalibrated camera? Can you still

recover the PSF an use it to correct the image? In fact, with a slight modiﬁcation, the previous

algorithms still work.

Instead of assuming a known calibration image, you can detect strong elongated edges

and ﬁt ideal step edges in such regions (Figure 10.9b), resulting in the sharp image shown

in Figure 10.9d. For every pixel that is surrounded by a complete set of valid estimated

neighbors (green pixels in Figure 10.9c), apply the least squares formula (10.1) to estimate

the kernel K. The resulting locally estimated PSFs can be used to correct for chromatic

aberration (since the relative displacements between per-channel PSFs can be computed), as

shown by Joshi, Szeliski, and Kriegman (2008).

Exercise 10.4 provides some more detailed instructions for implementing and testing

edge-based PSF estimation algorithms. An alternative approach, which does not require the

explicit detection of edges but uses image statistics (gradient distributions) instead, is pre-

sented by Fergus, Singh, Hertzmann et al. (2006).

10.2 High dynamic range imaging

As we mentioned earlier in this chapter, registered images taken at different exposures can be

used to calibrate the radiometric response function of a camera. More importantly, they can

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