KotaruGupta

Introduction

Visual navigation systems track the position and orientation of a moving camera by using a series of images captured by the camera. They have important applications in navigation, 3D object recognition and virtual/augmented reality [6]. Initial visual navigation systems required dedicated external markers like infrared light-emitting diodes [4]. Widespread adaptation of such systems was an expensive proposition because it involved installing precisely machined ceiling panels. Current visual inertial navigation systems [1, 2] achieve similar accuracy without requiring any external dedicated infrastructure. These systems use Inertial Measurement Unit (IMU) sensors which are rigidly attached to the camera along with a camera to track the camera. These systems use features available in natural images and do not need any dedicated external markers. With visual inertial navigation systems making way into our daily lives with navigation and augmented reality applications, it is important to understand the performance of these systems in typical indoor environments.

Background

Visual-inertial navigation systems have demonstrated error of less than 0.5 percent of the trajectory length in estimated the trajectory traced by a camera [3]. These systems have even been adopted by commercial systems like Google Tango and Microsoft Hololens. However, literature cites problems with reflective or texture-less objects, in dim light, with repeated patterns [5]. We want to test the performance of the system and quantify the performance degradation in these failure scenarios.

Results

In this section we report the results of the experiments carried out in three different settings:

1. Different physical environments.
2. Varying Spatial Frequency of the input image.
3. Varying texture of input image.

In all three cases we conduct two set of experiments.

1. We keep the Hololens stationary and measure variation in location reported by the Hololens.
2. We use a mechanical stage to displace the holo lens by 2 mm. We then calculate the difference between the initial and final position as reported by Hololens.

Different Physical Environment

We conducted the experiments in four different settings.

1. Lab Environment
2. Repeated Pattern
3. Texture less
4. Glass surface

Standard Deviation in position values for different Physical Environments

Relative Error for 2 mm Displacement for different Physical Environment

We can see from the results above that texture less surface is clearly a failure mode for the holo lens. Though it is a bit surprising that holo lens performs marginally better in case of repeated pattern and glass environment than lab environment.

Varying Spatial Frequency

We generate images with varying spatial frequency.Our goal is to create an image containing a single frequency component as much as possible. We choose a cosine signal with a low frequency cos(x). Our corresponding two dimensional function will be: $f(x,y)=cos(kx)*cos(ky)$ We then define a matrix and store the values of for different pairs to generate the images. The code for image generation can be found in the appendix section.

Standard Deviation in position values for varying Spatial Frequency

Relative Error for 2 mm Displacement for varying Spatial Frequency

We can see from the graph below that in case of both high and low spatial frequency the relative error is very high. This can be attributed to the fact that low frequency images correspond to texture less surface and high frequency surface corresponds to repeated pattern both of which seem to be a failure scenarios for holo lens.\

Plot of Relative Error vs Spatial Frequency

Varying Texture of Input Images

For this experiment we start with an image of random black dots on white background. We repeatedly smoothen the image using a Gaussian filter to get varying textures.

Standard Deviation in position values for different Textures

Relative Error for 2 mm Displacement for different Textures

We expected the relative error to increase as we increased the blurring. However, we notice that in case of blurring 10,000 times the relative error is lower as compared to blurring 100 times. As we repeatedly apply blurring the contrast of the image is also changing which might have counter affect to decrease the relative error.

References

[1] J. Engel, V. Koltun, and D. Cremers. Direct sparse odometry. arXiv preprint arXiv:1607.02565, 2016. 

[2] J. A. Hesch, D. G. Kottas, S. L. Bowman, and S. I. Roumeliotis. Consistency analysis and improvement of vision-aided inertial navigation. IEEE Transactions on Robotics, 30(1):158–176, 2014. 

[3] C. Cadena, L. Carlone, H. Carrillo, Y. Latif, D. Scaramuzza, J. Neira, I. D. Reid, and J. J. Leonard. Past, present, and future of simultaneous localization and mapping: Towards the robust-perception age. arXiv preprint arXiv:1606.05830, 2016. 

[4] G. Welch, G. Bishop, L. Vicci, S. Brumback, K. Keller, et al. The hiball tracker: High-performance wide-area tracking for virtual and augmented environments. In Proceedings of the ACM symposium on Virtual reality software and technology, pages 1–ff. ACM, 1999. 

[5] A. Yates and J. Selan. Positional tracking systems and methods, May 2016.

[6] G. Welch and E. Foxlin. Motion tracking survey. 2002.

Appendices

Appendix I

Appendix II