﻿ 基于非稳态随机过程的近红外反射率鲁棒估计算法
 控制与决策  2019, Vol. 34 Issue (6): 1151-1159 0

### 引用本文 [复制中英文]

[复制中文]
FANG Zhuo-qun, YU Xiao-sheng, JIA Tong, WU Cheng-dong, LI Yong-qiang, XU Ming. Nonstationary stochastic process-based robust estimation algorithm of near-infrared albedo[J]. Control and Decision, 2019, 34(6): 1151-1159. DOI: 10.13195/j.kzyjc.2017.1617.
[复制英文]

### 文章历史

1. 东北大学 信息科学与工程学院，沈阳 110004;
2. 东北大学 机器人科学与工程学院，沈阳 110004

Nonstationary stochastic process-based robust estimation algorithm of near-infrared albedo
FANG Zhuo-qun 1, YU Xiao-sheng 2, JIA Tong 1, WU Cheng-dong 2, LI Yong-qiang 1, XU Ming 1
1. College of Information Science and Engineering, Northeastern University, Shenyang 110004, China;
2. Faculty of Robot Science and Engineering, Northeastern University, Shenyang 110004, China
Abstract: Albedo estimation plays an important role in many areas such as computer vision, computer graphics etc. A robust estimation algorithm of near-infrared albedo (RENA) based on nonstationary stochastic process is proposed in order to obtain albedo with high quality. This algorithm takes Kinect one as input and establishes an additive noise model of albedo. Simultaneously, the concept of robust shading estimation is proposed to simplify the nonstationary stochastic process model of albedo. Experiments show that estimation results of the proposed algorithm are better than other denoising algorithms, and it is suitable for high precision estimation of albedo images in indoor scenes.
Keywords: near infrared    albedo    robust estimation    stochastic process    depth image    infrared image
0 引言

1 相关工作

1.1 本征分解方法

1.2 主动测量方法

1.3 本征优化方法

RENA算法属于主动测量方法, 通过使用简单方便的Kinect二代传感器, 可以轻松实现对室内场景的反射率测量[2].同时, 通过对反射率图像的非稳态随机过程建模, 应用鲁棒估计算法提供低计算复杂度的高精度反射率图像估计.

2 光照模型与算法流程 2.1 Lambertian光照模型

Lambertian光照模型是漫反射的理论模型.在此基础上建立Kinect近红外光照模型, 依据Kinect传感器的近红外投影仪内部结构, 将其近似为点光源.又因为投影仪与近红外相机的距离较小, 较之于Kinect的拍摄距离可以忽略不计, 所以近似认为近红外光源与相机在同一位置.基于以上假设, Kinect的Lambertian光照模型如图 1所示.

 图 1 Lambertian光照模型

 (1)

 (2)

 (3)
2.2 算法流程

 图 2 系统流程

3 反射率图像鲁棒估计

3.1 非稳态随机过程模型

3.2 光照度与反射率初值测量

 (4)

 (5)

3.3 加性噪声模型

 (6)

 (7)

 (8)

 (9)

 (10)

 (11)

3.4 最小均方误差算法

 (12)

 (13)

 (14)

 (15)

σi, j2(A)和σi, j2(η)分别是非稳态光照度信号和噪声方差.而噪声方差可以表示为

 (16)

σi, j2(||v||2)和σi, j2(κ)分别是深度误差方差和光强分布误差方差.又因为E(A(0))=E(A), 所以

 (17)

 (18)

 (19)

σi, j2(ρ)和σi, j2(ω)分别是反射率非稳态信号和噪声方差.其中

 (20)

σi, j2(n)和σi, j2(s)分别为表面法向误差方差和入射光反方向误差方差.类似于光照度期望和标准差, 可以采用同样的方法计算反射率期望和标准差.综上, 根据式(18)~(20)即可计算出优化反射率, 反射率估计公式也符合去噪的客观规律.

Step 1:使用深度和光强分布的测量值计算初始光照度

Step 2:通过线性组合光照度期望与初始光照度, 估计优化光照度

Step 3:根据优化光照度、表面法向和光源方向计算初始反射率

Step 4:通过线性组合反射率期望与初始反射率, 估计优化反射率

4 实验分析

4.1 评价标准

MSE是图像中反射率估计值与真值的均方误差, 这里采用与尺寸无关的计算方式.具体计算时, 图像绝对亮度的调整适应最小误差.

LMSE是反射率的局部均方误差.取反射率图像大小10 %的窗口沿图像长边有重叠地滑动取样, 计算每个取样窗口的局部MSE.最后加权平均各窗口的局部MSE, 获得LMSE结果.

DSSIM是结构相似性(SSIM)的一种变形, 衡量图像的不相似度, 具体形式为(1-SIMM)/2.这里用于比较反射率估计值与真值的结构差异性, 其值越小越好.

4.2 结果与分析

RENA算法以非稳态随机过程为理论基础建立图像去噪模型, 其实质相当于一个图像去噪算法.因此, 采用双边滤波、中值滤波和维纳滤波3种图像去噪算法作为对比.为了充分验证算法性能, 实验中对人工噪声场景和真实噪声场景两种带有噪声的反射率图像进行反射率估计.

 图 3 人工噪声场景实验结果对比
 图 4 反射率期望和标准差

RENA算法中的多个误差方差都是与设备相关的, 为了采集RENA算法所需的参数, 采用对单个Kinect二代传感器进行事先标定的方法获取误差方差.通过对白色墙面进行多次连拍, 计算σi, j2(s)和σi, j2(κ); 通过对多个简单静态场景的连拍图像, 计算σi, j2(||v||2); 通过对场景表面法向算法[19]的邻域阈值进行调整, 获取σi, j2(n).

 图 5 用于初始反射率估计的测量值
 图 6 特定的真实噪声场景实验结果对比

 图 7 室内的真实噪声场景实验结果对比1
 图 8 室内的真实噪声场景实验结果对比2

5 结论

RENA通过使用Kinect二代传感器, 实现对室内场景的初始反射率测量, 应用鲁棒估计算法降低由于表面法向误差和深度测量误差引入的噪声, 从而提供低计算复杂度、高精度反射率图像估计.通过对多个室内场景的反射率测量实验, 表明该算法适用于快速估计室内场景的反射率图像.但是, RENA算法采用的期望和方差数据需要通过标定Kinect设备才能获取, 这些数据又因设备而异, 这给应用多台Kinect设备进行反射率测量带来不便.未来计划探索一种通用于不同Kinect设备的反射率测量优化方法.

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