Fundamentals of Digital Image Processing

Author：Solomon, Chris，Breckon, Toby

Image Acquisition of Digital Camera

• • 1. Introduction

The concept of the digital image was first introduced in the transportation of the digital image using submarine cable system in the early twenty century [3]. In addi- tion, the advance in the computational hardware and processing unit lead to the development of modern digital image processing techniques. Specifically, the digital image processing started in the application field of remote sensing.In 1964, the Jet Propulsion Laboratory applied the digital image processing technique to improve the visual quality of the transmitted digital image by Ranger 7 [1, 3]. In the medical imaging, the image processing techniques were applied to develop the computer- ized tomography for medical imaging devices in early 1970s, which generates a two-dimensional image and three-dimensional volume of the inside of the object by passing the X-ray [3]. In addition to the remote sensing and medical imaging, the digital image processing techniques have been widely used in various application fields such as consumer electronics, defense, robot vision, surveillance systems, and artificial intelligence systems.

In the modern image acquisition system, the image signal processing (ISP) chain plays an important role to obtain the high-quality digital image as shown in Fig. 1.1. The light pass the lens and color filter array (CFA). Since the imaging sensor with- out the CFA absorbs the light in all spectrum bands, we cannot obtain the color information. To generate the color image, the digital camera uses the common CFA called Bayer pattern, which consists of two green (G), one red (R), and one blue

(B) filter because the human visual system is more sensitive to the light in the green wavelength [2]. The advanced CFA replaces the one green filter with white filter to increase the amount of light.

copy; Springer Nature Singapore Pte Ltd. 2018 3

A. Vyas et al., Multiscale Transforms with Application to Image Processing, Signals and Communication Technology, https://doi.org/10.1007/978-981-10-7272-7_1

Fig. 1.1 The block diagram of the image signal processing chain

converts the electrical charges to the electric analog signal. The analog front end (AFE) module of ISP chain performs the sampling and quantization processes to convert the analog signal to the digital signal. Sequentially, the AFE module also controls the gain of the acquired signal to increase the signal-to-noise ratio (SNR). In low-illumination condition, since the amount of the photons is decreased to react an imaging sensor, the digital image having low contrast is acquired with low SNR [4, 5, 7, 8]. In addition, the recent imaging devices increases the spatial resolution of a digital image by drastically reducing the physical size of each pixel. However, the reduced pixel size results in the chrominance noise called the cross-talk because of the interference of the photons among the pixels and it also reduces the SNR in each color channel.

The digital back end (DBE) module performs the digital image processing tech- niques to improve the quality of an input image. First, the DBE module performs the demosaicing to separate the color information from the raw image data by using the interpolation algorithms [6]. In addition, the image enhancement techniques are performed to improve the dynamic range of an image. The auto white balance (AWB) performs the color constancy, which makes the digital image be acquired under the neutral light condition by correcting the chromaticity. Finally, the noise reduction should be performed to remove the amplified noise in the image enhancement process. Additionally, since the demosaicing and noise reduction techniques may decrease the quality of the image by the blurring and jagging artifacts, the image restoration techniques called super-resolution can be performed to obtain the high-resolution image.

Sampling

The sampling and quantization are major processes performed in the AFE module of ISP chain to convert a continuous image signal to a series of discrete signals. In this section, we briefly describe the mathematical background of the sampling theorem.

Fig. 1.2 The sampling operation of a continuous function using an impulse train: a 1D continuous function, b impulse train with period T , and c the sampled function by the multiplication of a and b

Let x(t) be a one-dimensional (1D) continuous function, the sampling operation can be regarded as the multiplication of x(t) and impulse train p(t) with period T , for k = ··· , minus;2, minus;1, 0, 1, 2,.. ., as

(1.2.1)

Figure 1.2 shows the sampling operation of an 1D continuous function using an impulse train. As shown in Fig. 1.2, a continuous function is sampled with interval T and the amplitude of an impulse train varies with that of the continuous function x(t). The black dots represent the sampled values of x

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数字图像处理基础

作者：所罗门-克里斯、布雷肯-托比

1.1数码相机的图像采集

1.1.1介绍

数字图像的概念于20世纪初首次引入到海底电缆系统的数字图像传输中[3]。此外，计算硬件和处理单元的进步也带动了现代数字图像处理技术的发展。具体来说，数字图像处理开始于遥感应用领域。1964年，喷气推进实验室应用数字图像处理技术，以提高Ranger 7发射的数字图像的视觉质量[1, 3]。在医学成像中， 20世纪70年代初，图像处理技术被应用于医学成像设备的计算机层析成像中，在物体内部通过X射线产生了二维图像和三维体影[3]。除了遥感和医学成像之外，数字图像处理技术也被广泛应用于各种应用领域，如：消费电子、国防、机器人视觉、监控系统和人工智能系统。

在现代图像采集系统中，图像信号处理(ISP)链对于获得高质量的数字图像起着重要的作用，如图1.1所示。光线通过镜头和滤色片阵列(CFA)。因为没有CFA的成像传感器可以吸收所有光谱波段的光，因此无法获得颜色信息。为了产生彩色图像，数码相机使用普通的CFA称为拜耳图案，它由两个绿色(G)，一个红色(R)组成，还有一个蓝色(B)过滤，因为人类视觉系统对绿色波长的光更敏感[2]。先进的CFA取代一个绿色滤光器的白色滤光器，以增加光量。

斯普林格自然新加坡有限公司2018年

1. Vyas等人，多尺度变换运用在图像处理、信号和通信技术中的应用https://doi.org/10.1007/978-981-10-7272-7_1

RGB图像

降噪

自动白平衡

自动对焦

去马赛克

数字后端

编 码

离散信号

模拟前段

透镜

模拟信号

CFA

传感器

图1.1图像信号处理链的框图

将电荷转换为模拟电信号。ISP链的模拟前端(AFE)模块执行采样和量化处理，将模拟信号转换为数字信号。接着，AFE模块还控制获取的信号的增益以提高信噪比。在低光照条件下，由于光子的数量减少到响应成像传感器，获得低信噪比[4，5，7，8]低对比度的数字图像。此外，最近的成像设备通过大幅减少每个像素的物理尺寸来提高数字图像的空间分辨率。 然而，由于像素间光子的干扰，使得像素尺寸减小，导致色度噪声被称为相声噪声，同时也降低了各彩色信道的信噪比。

数字后端(DBE)模块执行数字图像处理技术以提高输入图像的质量。首先，DBE模块执行去噪操作，使用插值算法将颜色信息从原始图像数据中分离出来[6]。此外，还执行图像增强技术以提高图像的动态范围。自动白平衡(AWB)实现了颜色的恒定性，通过校正色度，使数字图像在中性光条件下得到。最后，对图像增强过程中的放大噪声进行降噪处理。此外，由于去噪和降噪技术可能会因模糊和干扰伪影而降低图像质量，为了获得高分辨率的图像，可以采用所谓的超分辨率图像恢复技术。

1.2 抽样

在ISP链的AFE模块中，采样和量化是将连续图像信号转换成一系列离散信号的主要过程。在这一部分中，我们简要描述了抽样定理的数学背景。

图1.2使用脉冲序列的连续函数的采样操作：a一维连续函数，b周期为T的脉冲序列，以及c通过a和b相乘得到的采样函数。

设x(T)是一维(1D)连续函数，当k=...，minus;2，minus;1，0，1，2时，采样运算可视为x(T)与周期T的脉冲列p(T)的乘积，同样的

(1.2.1)

图1.2显示了使用脉冲序列的一维连续函数的采样操作。如图1.2所示，用间隔T采样连续函数，脉冲序列的振幅随连续函数x(T)的振幅而变化。黑点表示在KT位置的x(T)的采样值。

由于脉冲序列是周期T的周期函数，所以它可以用Fourier级数展开表示为

(1.2.2)

当

(1.2.3)

脉冲序列的傅里叶变换是用(1.2.2)定义的。

(1.2.4)

其中P(u)是p(t)的傅里叶变换。脉冲序列的傅里叶变换是周期为1/T的脉冲序列。此外，由于傅里叶变换函数在空域上的乘法是频域的卷积，所以采样函数在(1.2.1)中的傅里叶变换可以实现。 表示为

(1.2.5)

其中，表示采样函数的傅里叶变换。采样函数的傅里叶变换也是周期为1/T的位置为k/T的x(t)的傅里叶变换序列。

图1.3显示了在不同采样率1/T的频域中如何采样连续函数。图1.3a是连续函数x(T)的Fourier变换形式，它使用中的带限滤波器进行滤波。图1.3b显示了采样率较高的采样函数的傅里叶变换。由于采样信号完全分离，可以使用图1.3a中使用的带限滤波器从重构X(u)。

图1.3不同采样率的比较结果：a带限连续函数的傅里叶变换，b用lt;2 umax实现采样函数的傅里叶变换，c用gt;2 umax实现采样函数的傅里叶变换

另一方面，如果以较低的采样速率采样带限信号，则采样函数的傅里叶变换重叠，如图1.3c所示。这意味着抽样操作在采样率高于最大频率umax两倍的情况下，以完全重建X(u)。这被称为奈奎斯特-香农抽样定理。

gt;2 umax (1.2.6)

在二维情况下，可以使用二维脉冲序列进行采样。给定二维连续函数x(t，q)和脉冲列p(t，q)，二维采样函数xs(t，q)可以是写成

(1.2.7)

由于二维脉冲列是一个周期函数，因此可以将傅里叶级数展开表示为(1.2.2)中的一维脉冲列。二维脉冲列的傅里叶级数展开定义为

(1.2.8)

在

(1.2.9)

p(t，q)的傅里叶变换定义为

(1.2.10)

二维脉冲序列的傅里叶变换是周期为1/T和1/q的周期脉冲序列。设xs(u，v)是二维采样函数xs(t，q)，xs(u，v)的Fourier变换 )可以用频域卷积定理进行估计，如

(1.2.11)

图1.4周期为1/T和1/q的采样函数在频域中的频谱

以与1D情况中的采样相同的方式，在空间域中的采样的傅立叶变换导致在该位置处的频谱X(U，V)的乘法复制版本。 K/T和l/Q图1.4显示了周期为1/T和1/Q的采样函数在频域的周期频谱。

为了重建原始的二维连续信号，必须满足尼奎斯特-香农采样率的要求。

gt;2 umax (1.2.12)

与

lt; 2v_max . (1.2.13)

其中Umax和Vmax分别代表u方向和v方向采样频谱的最大频率。图1.5显示了使用采样率低的采样函数的频谱 r分别是u方向和v方向最大频率的两倍。

图1.5采样函数与采样率的傅里叶变换比Nyquist-Shannon采样率：a采样函数的频谱使用 gt;2 umax，b采样函数的频谱使用 lt; 2v_max

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