ARIADNA Study 12-5101
Probabilistic Computing for Efficient Robotic Vision in Space
Type of activity: Standart study (25 k€)/p>
Background and motivation
1.1 General goal
In space robotics, the computational efficiency of algorithms is at a prime: tasks such as autonomous landing or rover navigation require a quick and efficient determination of actions, given an amount of energy and processing capacity, that is much more stringent than in earth-based scenarios.
This study focuses on a novel integrated software and hardware approach for reducing the computational effort and energy expenditure of computer vision algorithms. It is based on a combination of local sampling on the software side and probabilistic computing on the hardware side.
Specifically, on the software-side, the study will investigate random local sampling techniques that reduce the number of necessary computations at the cost of a slightly lower accuracy, to be done mainly by the ACT researchers. On the hardware-side, the study will investigate probabilistic computing as a means of saving energy at the cost of occasional errors in the calculations.
This proposal is addressed at research groups with expertise in probabilistic computing.
1.2 Software – efficient and robust algorithms.
Visual attention models could form a successful strategy for reducing the computational effort of computer vision algorithms. The central idea of visual attention models is that they devote most of the processing to the most relevant parts of the image. Surely, the main challenge is to automatically determine what is `relevant'. Several models have been devised that can determine relevant parts of an image, but many of them extensively process the entire image for determining regions of interest, inadvertently still leading to a large computational burden [1, 2, 3].
In order to achieve a higher computational efficiency, many attention models perform visual tasks on the basis of a restricted number of local samples [4,5,6,7]. In particular, these studies focus on informed sampling, in which the information from the current sample is used to select the next. This can lead to large computational efficiencies, but also often creates a challenging Partially Observable Markov Decision Problem (POMDP). Such a POMDP is currently difficult to solve, and the mentioned studies either make strong assumptions on the task  or have to train a model for each different task .
In this study the more straightforward strategy of random sampling is employed. It has been demonstrated that in some cases random sampling suffices to obtain speed-ups in the order of a 100 times with an unnoticeable cost in accuracy [8,9,10,11]. Below a figure illustrates this for an application of pitch and roll estimation of an Unmanned Air Vehicle that processes local image samples to find the horizon line. The y-axis represents the absolute error in each estimate, the x-axis the number of samples, with full sampling on the far right. It can be observed that most performance is gained after a 1000 samples the performance does not noticeably improve. Extracting only 1000 samples results in a speed-up of 14 times for a small image of 160 x 120 pixels (a border of 10 pixels is used in these specific experiments).
Figure 1: Number of samples extracted from an image versus average absolute errors in the estimates of the pitch and roll angle. The solid lines are for the results in which a linear algebraic solution is used for estimating the horizon (LA), the dashed lines are for the results with a linear perceptron.
1.3 Hardware – probabilistic computing.
If one accepts that vision algorithms can gain in efficiency by using only part of the information in an image, one can extend this reasoning to the hardware involved in the calculations to save even more time / energy. In typical processor hardware considerable amounts of energy are spent on obtaining correct calculation results, e.g., for adding or multiplying numbers. In probabilistic computing [12,13,14], the energy spent by the processing units is lowered, resulting in an increase of the probability that some operations might go wrong. Fortunately, it has been shown that the amount of energy saved is significantly larger than the amount of probability traded in  - see the figure below. As a consequence, in theory, large energy gains (in the order of 5 times) can be obtained at a minimal cost in calculation errors.
Figure 2: Energy expenditure versus the probability p that calculations will be incorrect. Figure adopted from .
Different applications of probabilistic computing have been
investigated. The study in  focused on the application of
probabilistic computing to the calculation of the Fourier
transform, showing that for human subjects the probabilistic
reconstruction is visually identical to the error-free one.
Another study involved the application of probabilistic
computing to Continuous Restricted Boltzmann Machines (CBRM)
. Such CBRMs normally require the generation of
pseudo-random numbers. Instead, in  probabilistic computing
naturally provided random numbers.
This study proposes to perform research on probabilistic computing in a different context, namely that of a vision algorithm for robotics. The main idea behind the application is that a slight loss in accuracy in the computations of the vision algorithms can still lead to robust and successful retrieval of information on the environment.
2. Research approach.
The research approach is to study the application of probabilistic computing in the context of a specific vision algorithm. Section 2.1 explains the stereo-vision algorithm that will serve as a starting point for the research. Section 2.2 addresses the research activities for the probabilistic computing part.
2.1. Specific vision algorithm: stereo-vision.
The extraction of information on the three-dimensional structure of the world is important to almost all robotic applications. The current Mars Rovers mainly rely on stereo-vision: the extraction of depth from two images made by two cameras positioned at a known distance from each other.
In the last decade, there has been a considerable progress in stereo-vision algorithms. On the one hand, there have been more successful applications of robotic stereo-vision, for example [15,16]. On the other hand, many techniques have been introduced to improve the accuracy of stereo-vision algorithms, cf. [17,18].
The most basic stereo vision algorithm takes a window from image 1 at position (x,y) and compares it with windows from image 2 at positions (x+?x,y) for various ?x. The comparison typically involves the sum of the squared differences between (grey-scale) pixel values:
Where i and j are coordinates within a window W, I1 contains the grey-values of the first image and I2 contains the grey-values of the right image. The ?x leading to the lowest C-value represents the disparity at (x,y) in image 1 and is a measure for the distance of the object seen at that image location. Most of the recently introduced more accurate methods combine the so-obtained local disparities with global constraints. One common method  is to segment image 1 (on the basis of colour and / or texture) and assume that each segment conforms to a certain model. For example, one can assume that each segment conforms to a plane. The disparities in the segment then serve as data for a plane fitting process, which smoothens out many of the local errors.
In this project, it is proposed to speed up the calculation of stereo-vision with the following method: instead of determining a disparity for every image location in image 1, only a subset of the locations is processed. In order to fit a plane through a segment, at least three disparities are necessary. To get a robust estimate, more samples are advisable, yet it is not necessary to determine the disparities for all pixels in the segment. Determining fewer disparities leads to fewer computations, but results in a less accurate estimate of the plane parameters. As in other cases of (random) sampling, we expect the trade-off between the number of samples and the accuracy of the estimates to be rather gentle: allowing significant speed-ups at a negligible cost in accuracy.
2.2 Probabilistic processing architecture.
The bulk of the stereo-vision processing consists of calculating equation 1. The idea is to implement the related calculations in a specifically designed probabilistic processing architecture.
Proposals should include argued choices concerning the
- Different designs are possible for the components that will perform addition / subtraction / multiplication. One example is that in an adder, all bits can be provided with the same voltages, or higher voltages can be applied to the higher order bits (as in the BIVOS approach ). Another example is that instead of variable voltages and a traditional representation of integers, a different representation of numbers can be employed in combination with a single voltage for all bits.
- The proposal should clarify which methodology is proposed. In particular, it should address the connection between the probabilistic computing architecture and the stereo-vision algorithm. The stereo-vision algorithm will be implemented in MATLAB. In a first possible methodology, the work is split in two independent parts. The hardware group then identifies for each operation in equation 1 the probabilities and types of errors that can occur at different voltages. These errors can then be modelled in the MATLAB scripts. A second possible methodology would be to couple the MATLAB stereo-vision script with hardware simulator software: calculations would then be done directly by the simulated hardware. A third possible methodology is to have actual hardware in the loop. The first methodology is the baseline requirement for the study. In any case, the chosen methodology should provide for a way to compare the amount of energy consumed in a probabilistic and a non-probabilistic scenario.
- The design should address how the dedicated probabilistic computing parts for addition / subtraction / multiplication fit within a further non-probabilistic CPU / DSP. How would they interface and does sending numbers to these dedicated probabilistic processing components incur additional costs?
Considerations given to radiation effects would be a welcome though not essential addition to the study.
The main objectives of this study are:
(1) To research a probabilistic processing architecture that would best fit the stereo-vision algorithm. Specifically, this involves the optimization of a design of an adder, subtractor, and multiplier. The designs should be optimized for operating at voltages that are as low as possible in combination with error probabilities and error magnitudes that remain within a reasonable range.
(2) To evaluate the energy efficiency gained by employing the probabilistic processing structure, and analyse its relation to the performance (in terms of the probability and size of the calculation errors and in terms of the 3D reconstruction).
4. Collaboration with the Advanced Concepts Team of ESA
The study is addressed at a research group with expertise in probabilistic computing. The research will be conducted in close cooperation with ACT researchers.
The ACT will contribute to the research project the knowledge of stereo-vision algorithms, including the necessary code. This will constitute the basis for exploring the way in which probabilistic computing can be applied. It is expected that analysis from a probabilistic computing point of view could lead to adjustments of the stereo-vision algorithm. The end goal of the interaction is a stereo-vision algorithm that in combination with a probabilistic computing architecture should exploit the trade-off between energy and reconstruction result and lead to at least an order of magnitude of efficiency improvement with respect to standard approaches.
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