>>Robust Machine Vision: Feedback Control in Image Processing

### Robust Machine Vision: Feedback Control in Image Processing

Traditionally, vision systems are open-loop sequential operations, which function with constant predefined parameters and have no interconnections between them. This approach has impact on the final 3D reconstruction result, since each operation in the chain is applied sequentially, with no information between the different levels of processing. In other words, low level image processing is performed regardless of the requirements of high level processing. In such a system, for example, if the segmentation module fails to provide a good output, all the subsequent steps will fail.

The basic diagram from which feedback mechanisms for machine vision are derived can be seen in the above figure. In such a control system, the control signal u, or actuator variable, is a parameter of an image processing operation, whereas the controlled, or state, variable y is a measure of processing quality.

##### Motivation

In a robotic application, the purpose of the image processing system is to understand the surrounding environment of the robot through visual information. Usually, an object recognition and 3D reconstruction chain for robot vision consists of low and high levels of processing operations. Low level image processing deals with pixel wise operations aiming to improve the input images and also separate objects of interest from background. Both the inputs and outputs of the low level processing blocks are images. The second type of modules, which deal with high level visual information, are connected to low level operations through a feature extraction component which converts the input images to abstract data describing the imaged objects. The importance of the quality of results coming from low level stages is related to the requirements of high level image processing. Namely, in order to obtain a proper 3D virtual reconstruction of the imaged environment at a high level stage, the inputs coming from low level have to be reliable.

##### An Extremum Seeking Control Approach
$\dot{\text{\textbf{\textit{x}}}}(k) = f [\text{\textbf{\textit{x}}}(k), \text{\textbf{\textit{u}}}(k)],$ $\text{\textbf{\textit{y}}}(k) = g [\text{\textbf{\textit{x}}}(k)]$

where $\text{\textbf{\textit{x}}} \in \Re^n$ is the state vector, $\text{\textbf{\textit{u}}} \in \Re$ is the actuator (input), $\text{\textbf{\textit{y}}} \in \Re$ is the output vector, $f: \Re^n \times \Re \rightarrow \Re^n$ is the state transition function and $g: \Re^n \rightarrow \Re$ is the output function. $k$ represents the discrete time. Suppose that we have a control law:

$\text{\textbf{\textit{u}}}(k) = \alpha [\text{\textbf{\textit{x}}}(k), \theta]$

the control problem is to find the optimal parameter $\theta^*$ which provides an output of desired, or reference, quality. Following the above reasoning, the closed-loop system:

$\dot{\text{\textbf{\textit{x}}}} = f[\text{\textbf{\textit{x}}}, \alpha (\text{\textbf{\textit{x}}}, \theta)]$ $\theta^* = \text{arg min } \text{\textbf{\textit{x}}}(k) \text{ } \text{ or } \text{ } \theta^* = \text{arg max } \text{\textbf{\textit{x}}}(k)$

The choice of this particular type of control method lies in the fact that, taking into account the non-linearity of an image processing system, it is difficult to determine reference values that could be applied to classical feedback structures. Hence, in the image processing control approach, the desired state of a vision system is given by the extremal values of the state vector. The proposed model is applied to the depth estimation processed.

##### References

S.M. Grigorescu, G. Macesanu, T.T. Cocias, D. Puiu and F. Moldoveanu "Robust Camera Pose and Scene Structure Analysis for Service Robotics", Robotics and Autonomous Systems, Elsevier, Netherlands, vol. 59, no. 11, pp. 889-909, 2011.

S.M. Grigorescu Robust Machine Vision for Service Robotics, Institute of Automation, University Bremen, Shaker-Verlag, Aachen, 2010.

##### Latex Bibtex Citation
@article{grigorescu2011robust,
author = {Grigorescu, Sorin M and Macesanu, Gigel and Cocias, Tiberiu T and Puiu, Dan and Moldoveanu, Florin},
title = {Robust camera pose and scene structure analysis for service robotics},
journal = {Robotics and Autonomous Systems},
volume = {59},
number = {11},
pages = {899--909},
year = {2011},
publisher = {Elsevier},
}