Finding location using omnidirectional video on a wearable computing platform

Wasinee Rungsarityotin, Thad E. Starner
College of Computing, GVU Center,
Georgia Institute of Technology
Atlanta, GA 30332-0280 USA
{wasinee|testarne}@cc.gatech.edu

• Abstract
• Introduction and Previous Work
• Our Approach
• The Method
• Image Measurement
• The Likelihood model
• The Motion Model
• The Condensation algorithm
• Initial condition
• Initialization and Recovery
• Experimental Results
• Finding the likelihood: A case of strong prior
• Tracking
• Conclusion and Future Work
• Acknowledgements
• Bibliography
• About this document ...

Abstract

In this paper we present a framework for a navigation system in an indoor environment using only omnidirectional video. Within a Bayesian framework we seek the appropriate place and image from the training data to describe what we currently see and infer a location. The posterior distribution over the state space conditioned on image similarity is typically not Gaussian. The distribution is represented using sampling and the location is predicted and verified over time using the Condensation algorithm. The system does not require complicated feature detection, but uses a simple metric between two images. Even with low resolution input, the system may achieve accurate results with respect to the training data when given favorable initial conditions.

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Introduction and Previous Work

Recognizing location is a difficult but often essential part of identifying a wearable computer user's context. Location sensing may be used to provide mobility aids for the blind [13], spatially-based notes and memory aids [18,17,8], and automatic position logging for electronic diaries (as used in air quality studies [6]).

A sense of location is also essential in the field of mobile robotics. However, most mobile robots combine extrinsic (environmental) sensors such as cameras or range sensors with their manipulators or feedback systems. For example, by counting the number of revolutions of its drive wheels, a robot maintains a sense of its travel distance and its location based on its last starting point. In addition, many robots can close the control loop in that they can hypothesize about their environment, move themselves or manipulate the environment, and confirm their predictions by observation. If their predictions do not meet their observations, they can attempt to retrace their steps and try again.

Determining location with the facilities available to the wearable computer provides an additional challenge. Accurate, direct feedback sensors such as odometers are unavailable, and many sensors typical in mobile robotics are too bulky to wear. In addition, the wearable has no direct control of the user's manipulators (his/her feet) and consequently is forced to a more loosely coupled feedback mechanism.

In the wearable domain, small video cameras are attractive for sensing because they can be made unobtrusive and provide a great deal of extrinsic information. This is beneficial since we cannot instrument a person with as many sensors as we do a robot. A major challenge of using vision is to build a framework that can handle a complex multi-modal statistical model. A recent approach developed in both statistics and computer vision for problems of this nature is the Condensation algorithm, a form of the Monte Carlo algorithm that simulates a distribution by sampling.

Our approach to determining location is based on a simple geometric method that uses omnidirectional video for both intrinsic (body movement) and extrinsic (environmental changes) sensing. The Condensation algorithm combines these different types of information to predict and verify the location of the user. Inertial data, such as provided by a number of personal dead reckoning modules for the military, can be used to augment or replace the intrinsic sensing provided by the omnidirectional camera. We annotate a two dimensional map (the actual floor plan of the building) to indicate obstacles and track the user's traversal through the building. We attempt to reconstruct a complete path over time, providing continuous position estimates as opposed to detecting landmarks or the entrance or exiting of a room as in previous work.

In the wearable computing community, computer vision has traditionally been used to detect location through fiducials [16,14,19,1]. More recently, an effort has been made to use naturally occurring features in the context of a museum tour [12]. However, these systems assume that the user is fixating on a particular object or location and expects visual or auditory feedback in the form of an augmented reality framework. A more difficult task is determining user location as the user is moving through the environment without explicit feedback from the location system. Starner et al. [20] use hidden Markov models (HMM's) and simple features from forward and downward looking hat-mounted cameras (Figure 6) to determine in which of fourteen rooms a user is traveling with 82% accuracy. Using a forward-looking hat mounted camera, Aoki et al. [10] demonstrate a dynamic programming algorithm using color histograms to distinguish between sixteen video trajectories through a laboratory space with 75% accuracy. Clarkson and Pentland [5] use HMM's with both audio and visual features from body-mounted cameras and microphones for unspecified classification of locations such as grocery stores and stairways. Continuing this work, Clarkson et al. [4] use ergodic HMM's to detect the entering and leaving of an office, kitchen, and communal areas with approximately 94% accuracy. Unlike these previous systems which identify discrete events, our system will concentrate on identifying continuous paths through an environment.

In computer vision, Black [2] and Blake [3] have used the Condensation algorithm to perform activity recognition. In mobile robot navigation, Thrun et al. [7] also use the Condensation algorithm with the brightness of the ceiling as the observation model. A camera is mounted on top of a robot to look at the ceiling, and the brightness measure is a filter response. The most recent work by Ulrich and Nourbakhsh [21] is most similar to ours in that they use omnidirectional video and require no geometric model. However, their goal is to recognize a place on a map, not to recover a path. In this sense, there is no need to propagate the posterior distribution over time and thus their nearest-neighbor algorithm is sufficient.

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Our Approach

Our main motivation is to demonstrate a vision-based system that can determine location without fully recovering the 3D geometry of a scene. The input to the system is a low resolution image from a parabolic omnidirectional camera (Figure 6). We approach this problem using a Bayesian predictive framework that seeks the appropriate place and image from training data to describe what we currently see and infer a location.

The first stage in our approach is to capture images of the environment for training. The next stage is labeling of the training data. Because there is no explicit geometric modeling, we need to associate images with positions on an actual blueprint of the environment. The map must also represent obstacles such as walls to assist in the prediction of motion. This is done by the user editing the map to represent obstacles and valid travel areas. In Figure 1, valid areas were painted in gray on the actual blueprint and training paths were traced as series of black dots. We then create a probability model of how likely an image is observed from training paths. We first construct a joint density of the image similarity and distance on a map among training locations and derive the likelihood from the joint density.

We considered two simple image similarity metrics: the L2 norm and a color histogram. We chose the L2 norm because the color histogram did not provide enough discrimination. For example, in our data set, hallways did not have enough color variation to show significant differences in their respective color histograms.

On the other hand, a slight problem with using the L2 norm is maintaining rotational invariance so that different views taken from the same location look similar. We discuss the solution to this problem in Section 2.1.

Figure 1: An actual floor plan and a map with a valid area drawn in gray. The training paths are traced on the map in black lines.

(a)

(b)

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The Method

In a Bayesian framework, we want to find the posterior distribution conditioned on the image measurement $L$ at time $t$. Define a state at time $t$ as $\P^t = (x,y)$ a position on a 2D map and the observation as the image measurement $L$. Bayes's rule states that

$$p(\P^t\vert L) = \frac{p(L\vert\P^t)p(\P^t\vert\P^{t-1})}{p(L)}$$ (1)

We can assume that the probability of getting a measurement $p(L)$ is constant. Thus, the equation becomes

$$p(\P^t\vert L) \propto p(L\vert\P^t)p(\P^t\vert\P^{t-1})$$ (2)

where $p(L\vert\P^t)$ is the likelihood conditioned on the prediction and $p(\P^t\vert\P^{t-1})$ is a prior that incorporates a probabilistic motion model. The motion model must obey the first order Markov assumption, that the prediction depends only on the previous state. Because we rely on the similarity of two images to determine locations, finding the likelihood is about finding a good similarity metric $L$ and then use that to generate $p(L\vert\P^t)$ of the training data.

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Image Measurement

Because we are using low resolution images taken from a parabolic camera, finding good features to recover a person's movement is difficult (in this case, the situation is the same as the camera ego-motion problem). One easy choice is to use image similarity to identify a match and we use the $L_2$ norm. The limitation is that the learned model is not invariant over time. Thus, for the purpose of this study, we assumed that both training and testing were taken within two hours of each other.

We greatly benefit from having an omnidirectional camera because it allows us to use a normalized $L_2$ distance as a similarity metric. Assuming that changes caused by translation are negligible, we only need to make the $L_2$ metric invariant to rotation. We do this by incrementally rotating the image until we find a minimum error. This can be viewed as an image stabilization process.

Using the same definition for a state and observation, define the likelihood $p(L\vert\hat{\P}^{t}) = p(L\vert d_{t})$, where $\hat{\P}^{t}$ is a predicted position at time $t$, $L = \Vert I_{t} - I_{k}\Vert _{L2}$ the normalized $L_2$ norm, $d_{t} = \Vert\hat{\P}^{t} - \P_{k}\Vert$, and $\P_{k}$ is a state in the training data nearest to $\hat{\P}^{t}$. The next section will explain an experiment on finding the likelihood for the localization system. We will focus on modeling a case when the state (user's location) is near a training path (having distance on a map less than 10 pixels (3 feet per pixel) away).

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The Likelihood model

Figure 2: These figures show the estimation of $p(L\vert d)$ with (a) a histogram with uniform bin-size, (b) an exponential decay (Equation 3), (c) a Gaussian for each $d$ (Equation 4), and (d) a Gamma distribution for each $d$(Equation 5).

(a)	(b)
(c)	(d)

Figure 3: Figure (a) shows a two dimensional contour of Figure 2(a) illustrating that our density estimation has lower and upper limits (approximated by two curves in Figure (b)) that control the shape of the likelihood.

(a)

(b)

As seen in Figure 2, the likelihood is far from being a simple two dimensional function. Although the distribution appears noisy, it exhibits some structure as seen in the contour plot. Rather than performing a full minimization to solve for a closed form, we have chosen to estimate the likelihood with a combination of known distributions. To estimate the likelihood, first we compute a non-parametric form of the joint distribution $p(L,d)$ by uniform bin-size and it follows that $p(L^{t}\vert d) = \frac{p(L^{t},d)}{p(d)}$. Looking at a plot of $p(L^{t}\vert d)$ in Figure 2(a), we have observed that if the image distance $L^{t}$ is higher than 0.1, it is likely that the state is not a good match. We have used 0.1 as the standard deviation for the normal distribution and our experiment in Section 3.1 confirms that the above observation is reasonable.

In summary, we have tried three different functions to approximates the likelihood. Define the lower and upper limit of $p(L^{t},d)$ in Figure 3 as $\upsilon(d) = 0.5 - 0.415{e^{-0.17d}}$ and $\lambda(d) = 0.12-0.055{e^{0.26d}}$.

Let $p^{\prime}(L\vert d)$ be a parametric estimation of $p(L\vert d)$. We can define our three choices in terms of $L,d,\upsilon(d),\lambda(d)$ as:

1. an exponential decay independent of d where $N(\mu, \sigma^2)$ is a normal distribution,
   

   $$p^{\prime}(L\vert d) = N(0,10^{-2}), \forall L \geq 0$$ (3)

   
   

2. a normal distribution with the mean and variance controlled by $\upsilon(d)$ and $\lambda(d)$,
   

   $$p^{\prime}(L\vert d) = N(\frac{\upsilon(d) + \lambda(d)}{2},(\upsilon(d) - \lambda(d))^{2})$$ (4)

   
   

3. a gamma distribution with shape and rate controlled by $\upsilon(d)$ and $\lambda(d).$ Let $g(t,r, y)$ be a gamma distribution with shape parameter $t$ and the rate $r$. Define the likelihood $p(L\vert d)$ as a gamma distribution with; $\mu = \frac{\upsilon(d) + \lambda(d)}{2}, \sigma = \frac{\upsilon(d) - \lambda(d)}{4}$,
   

   $$p^{\prime}(L\vert d) = g(t, r, y), t = \frac{\mu^2}{\sigma^2}, r = \frac{\sigma^2}{\mu}$$ (5)

   
   

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The Motion Model

We tried two motion models. One was a dynamic model with position and velocity as random variables having Normal distributions. The second model was a simplified motion model of the parabolic camera. Without a high resolution input, a full recovery of ego-motion is a difficult problem even with an omnidirectional camera. Most of the algorithms presented in computer vision require good features to track. Given a low resolution imaging system such as ours (6), finding good features can be expensive.

To derive the simplified camera model, we took the same approach by Yagi et al. [22] with the assumption that the camera moves in a horizontal plane with constant height above the ground. We simplified the model more by only computing the motion of the ground-plane. The model has three degrees of freedom, translation ${t_x, t_y}$ and rotation $\alpha$ around the Z-axis. Because we only account for the motion of the ground-plane, motion in other planes will contain more error. To represent the uncertainty of the estimated motion, we distributed a set of samples around the solution and applied it to the Condensation algorithm. A random variable $\{t_x, t_y, \alpha\}$ was then transformed into a two dimensional space to be rendered on a map by rotating the translation vector ${t_x, t_y}$ by the angle $\alpha$.

Although we only mention estimating a person's displacement from a camera, the framework is not restricted to a single motion model. We could replace the recovery of the ego-motion with the inertial sensor or combine both. For our experiments, we only tried to estimate from the camera because we have a better way to quantify the uncertainty.

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The Condensation algorithm

The Condensation algorithm provides a framework that propagates the density over time and works with multimodal distributions that can be represented as sets of samples. In other words, the Condensation algorithm can be applied to a tracking problem where distributions of tracking parameters are not unimodal- unimodal distribution is visualized as having exactly one peak (not a ridge) such as the Normal distribution.

We give a summary of the algorithm below. For more information, [3] and [11] give an excellent overview of the method. Related algorithms are Importance Sampling [3,11] and Markov Chain Monte Carlo methods (MCMC) [15,7]. A review by Neal [15] provides a comprehensive review with attention to their applications to problems in artificial intelligence.

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Initial condition

Start with an initial position $\P^0$ and the prior density $p(\P^0)$. Let $\hat{\P}$ denote a prediction and $I^t$ be an image. To estimate $p(\P^t\vert L)$ at time t given the motion model $p(\hat{\P}\vert\P^{t-1})$ and the prior from the previous step $p(\P^{t-1}\vert I^{t-1})$, the Condensation algorithm states as follow:

1. Start with a set $S^{t-1}$ of $N$ samples that represents $p(\P^{t-1}\vert I^{t-1}).$
2. For all samples $\{s_i,\P_i^{t-1}\}$ with a position $\P_i^{t-1}$, make a prediction by applying a motion model $p(\hat{\P}\vert\P^{t-1}).$
3. Update the weight for each sample, for all $\{s_i,\hat{\P}_i\}$, $w_i = p(L_2\vert\hat{\P}_i).$
4. Sample from a discrete set of $\{\hat{\P}_i,w_i\}$ and iterate with this new set of samples that represents $p(\P^{t}\vert I^{t}).$

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Initialization and Recovery

Initial conditions for navigation can be determined by defining the prior density $p(\P^0)$. Alternatively, it is possible to allow the initial condition to approach a steady state in the absence of initial measurements. Provided that a unique solution exists and the algorithm can converge fast enough, we can populate an entire map with samples and let the Condensation algorithm [7] converges to the expected solution. For all of our experiments, an initial position $\P^0$ is manually specified by looking at the test sequence. In this case, we use a Gaussian for $p(\P^0)$ and thus direct sampling can easily be used. We can use a similar scheme to recover from getting lost-this is the same as finding a new starting point. Deciding that we are lost can be done by observing the expected distance from the training path or the expected weight assigned to samples. Decision regions for the confidence measure can be learned from the likelihood function. Empirically, we make a plot for both parameters and define a confidence region for being certain, uncertain, or confused. In Section 3.2, we will discuss how we define these decision regions from experimental results.

Figure 4: These figures show results from simulating the Condensation algorithm on one test sequence. The real event was that a person came in from the left side of a hall way continuing down the hall and turned right at about frame 147. A small cloud of samples at every time step shows that the localization system was confident and the path was correctly followed.

#112	#118	#124	#128
#132	#136	#140	#147

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Experimental Results

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Finding the likelihood: A case of strong prior

We use two independent test sequences to compare three functions. Additional testing on Equations 3 and 4 shows that the first choice performs much better than the others. One test sequence lasts about $1.5-3$ minutes. The Gaussian with varying parameters does not work at all, while the gamma function has an error rate of about $50\%$. Equation 3 performs much better than the others, with only a $10\%$ error rate.

For the training data, the results show that estimating $p(L\vert d)$ with exponential fall off gives the best result (Figure 2. This finding shows that if the similarity measure was high (low image difference), a new sequence would follow a training path and hence we can use the training data as the ground truth. For our data set, this prior was so strong that the exponential decay independent of $d$ worked well. This explained why the first choice, Equation 3 performed better than the rest. For other data sets, Equations 4 or 5 may work better. In summary, we approximate by choosing a parametric function that appears similar to the actual likelihood. A better way to learn the likelihood is to estimate a mixture of Gaussian or Gamma distributions.

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Tracking

Figure 5: Confidence measure obtained without motion estimation: based on a density plot, we divided the measurement $W$ into three regions as confidence when $W < 200$, uncertain when $200 < W < 800$ and confused when $W > 800$.

(a)

(b)

For experimental verification, we labeled all the test sequences to provide the ground truth. We randomly picked a starting position to avoid bias. We ignored the recovery problem by avoiding an area which we have not seen before. Two motion models were used: a simple random walk and the ego-motion of a camera. Examples of images taken from our omnidirectional parabolic camera are shown in Figure 6. We then masked out some visual artifacts caused by the ceiling, the camera and the wearer (Figure 6).

Figure 6: Multiple views, Input images and an image mask Three multiple views can be simultaneously captured using our vision-based system. The mask was used to eliminate visual artifacts caused by the ceiling and the wearer. All images were sampled down to $80\times 60$ pixels. Images in the first row were taken in a room with good lighting condition. Images in the second row were taken from a dim area. We decided to use the image similarity metric as the measurement because finding good features from these images was not reliable.

Table 1 summarizes the performance of our localization system running on one hundred cross-validation tests. A cross-validation is based on two different sequences of images taken from the same path, but acquired at different times. One of the sequences is used as training, while the other is used as test data. We generated a hundred test sequences by choosing one hundred segments from a nine-minute sequence. For each test, the starting position is known and the system tracks for one minute. Results from the simulation are samples weighted by the posterior distribution at each time step. They are shown as clouds of points propagating over time in Figure 4. Small clouds of samples indicate higher confidence.

For each test, the standard deviation of the likelihood model was 0.1 for the reason given in Section 3.1. We needed to capture at 30 Hz to recover the camera ego-motion, but the likelihood was only computed every sixth frame to increase efficiency. The task of the localization system is to keep track of a person's location and report a confidence measure. After one iteration of the algorithm, it reported a confidence measure as a cumulative weight of all samples. By observing the weight reported by the system, we defined three confidence types as confident, uncertain, or confused. Being uncertain means that a system has competing hypotheses. This results in one or more clouds of samples; in this case, the expected location may lie in a wall between two areas. Being lost implied that the system encountered a novel area or the likelihood was not giving enough useful information. In this case, the prediction was no longer useful. Although it may be possible to recover if a good match appears at a later time, no recovery method was implemented. One possible recovery method is to distribute samples over the entire map to find better candidates to continue tracking.

Table 1: The error rate with respect to different confidence types

Confidence type	Confidence	Uncertain	Confused
Random walk	4.57%	51.8%	83.89%
With motion estimation	20.23%	44.2%	78.3%

If the total reported weight was less than 200, we classified the system as being confident, from 200 to 800 as being uncertain, and beyond 800 being confused. For both tests with the random walk and motion estimation, the system was confident for 30% of the time, uncertain for 40% and confused for 29.5% (Table 1). With motion estimation, the error rate was improved for the uncertain case because additional knowledge was provided as to which hypotheses to choose. To show that our confidence measure was meaningful, we associated the measure with a deviation from the true path. If a deviation is more than 30 pixels from the actual path, then this is an error. The error rates were then reported for three confidence measures. As shown in the Table 1, when the system is very confident, the error rate is low. Two tests were performed to study if a motion estimation could reduce the uncertainty. While it did reduce the uncertainty, our simplified motion model introduced more noise to the system which results in an increase in the error rate even though the system is confident. More than anything, the high uncertainty and confusion is mainly contributed from having a sparse training set.

It took about three hours to complete a simulation of one hundred test sequences that added up to 100 minutes in real time. Thus, we expect an update rate for an on-line system to be about 2 Hz. With the current system, the most time consuming part for every sample is finding the nearest state from the training set. This can be greatly improved by using an adaptive representation of a 2D map such as an adaptive quad-tree or a Voronoi diagram.

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Conclusion and Future Work

In this paper, we have proposed a probabilistic framework for localization on wearable platforms using data collected from an omnidirectional camera. The framework based on the Condensation algorithm was formulated to determine the user's path without explicit feedback in the form of an augmented reality framework (e.g. fiducials). In addition to having the same challenges presented in continuous tracking of mobile robots, our system has to determine location with limited facilities available to the wearable computer.

On video recordings of real situations in an unmodified environment, we have demonstrated that our system can continuously track independent test sequences 95% of the time given a favorable starting location. The results show that a robust localization system will need a better motion model.

Future work should concentrate on combining intrinsic information from the camera with the inertia data and improving the statistical model of the observation to include multiple views. Starner et al. [20] use simple image measurement from forward and downward looking views as shown in the top row, while our system considers only the omnidirectional view. Measurements from all views can be combined through the observation model. Future implementations can also use the confidence measure to remain noncommittal and explore the solution space for a good location to restart the Condensation algorithm. Using this information allows the system to recover from situations where sufficient data to match does not exist. To handle changing environment we can extend Condensation to track time. We simply record the time that our training samples are taken. Since we know that the time of day cannot change drastically from one room to another, the local context affects of condensation and the comparison function still apply. Thus, time is simply another dimension that can vary as the algorithm walks through the building. A side result is not only does the system tell you where you are, but could also give an estimate on the time of day.

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Acknowledgements

We would like to thank Christopher Atkeson and Arno Schödl for helpful discussion on choosing the distance metric and probability models.

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Finding location using omnidirectional video on a wearable computing platform

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