Appearance-based segmentation of indoors/outdoors sequences of spherical views
Summary (2 min read)
Introduction
- I. I NTRODUCTION Navigating in large scale, complex and dynamic environments is a challenging task for autonomous mobile robots.
- Semantic representation consists in adding information about the places represented by nodes in the graph used at the topological level.
- Aplace, in this work, is therefore associated to a segment of the robot trajectory where the scene is sufficiently self similar,i.e. has the same structural properties extracted from the spherical views.
- The authors propose a novel representation relying on spherical harmonics which are particularly well-fitted to capture the structural properties in spherical views.
- Experimental results for indoor and outdoor environments are provided in section 4.
A. Definition
- The authors only detail the application of spherical harmonics to their problem.
- Fig. 3. The first five spherical harmonics bands are presented as unsigned spherical functions from the origin and by color on the unit sphere.
- Green corresponds to positive values and red to negative values.
- Due to the integral,fml coefficients exact computation can be very time consuming.
- This method is widely used in computer graphics for realtime lighting rendering.
B. Spherical harmonics as environment structure description
- Assuming that environment structure information is contained in the spherical image frequencies, pixel intensitie can be chosen as the samplesf(xi) values of the function f .
- The spectrum coefficientsfml are stacked into a vector which constitutes the global structure descriptor.
- In the case of the 2D discrete Fourier transform, the spectrum size is constrained by the image size.
- In the case of the spherical harmonics, nothing constraints the required number of bands.
- In [5], precise localization is achieved using only the first five bands.
A. Hypotheses and assumptions
- According to their place definition as a set of positions from which environment structure is similar, the authors aim to detect the significant changes in the global descriptor value along the sequence of spherical views.
- Changepoint detection is based on hypothesis testing: Null hypothesisH0 is the normal situation in which the observed parameters stick to the previous model.
- Let us assume thatf0 is the probability density function under hypothesisH0 and f1 underH1.
- The computation time is very low for a small t but increases rapidly with the number of observations.
- Density function estimation requires identically and independently distributed samples (i.i.d).
B. Online application
- As explained previously, the algorithm rapidly becomes time consuming and only one change-point detection is possible for a complete set of input observations.
- Considering the density function estimation constraints aforementioned, the sliding window has to be sufficiently large for a correct estimation.
- Spherical harmonics spectrum computation requires 290ms using the implementation described above (the sphere is sampled with 62500 samples uniformly distributed).
- A. Indoor experiment analysis Figure 6 presents the robot trajectory and the detected change-points.
- It is first interesting to notice that all changepoints correspond to important structure variations such as oorsteps or room volume variation (i.e. passing from a nook to a more open space).
B. Outdoor experiment analysis
- The algorithm presents a certain robustnessto rotation due to the sliding window reducing the environment sensed, but the spherical harmonics spectrum is not independent to any rotation.
- In a longer term, the segmentation algorithm could be coupled with a loop closure detection algorithm in order to improve change-point localization stability and with a semantic level by adding place classification and labelling.
- InIEEE/RSJ International Conf. on Intelligent Robots and Systems (IROS), 2011. [13].
- Localization in urban environments using a panoramic gist descriptor.
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Citations
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...1: Typical layers of a mapping system, courtesy of [Chapoulie et al. 2013]...
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...2012][Chapoulie et al. 2013], provide a topological segmentation based on change detection in the structural properties (textures, appearance frequency, orientation of straight lines, curvatures, repeated patterns) of the scene during navigation....
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...Environment mapping or model building is the process of constructing a one-to-one or many-to-one relationships between the 3D points in the real physical space and points in the digital space [11][36][35]....
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References
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285 citations
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...This level, with a higher degree of abstraction, allows us to specify contextbased navigation tasks in terms of queries [7]....
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221 citations
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...In computer graphics, only three bands are used due to an exponential attenuation in bands of higher frequencies [8]....
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...Further mathematical details about spherical harmonics can be found in [2], [1], [8]....
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192 citations
"Appearance-based segmentation of in..." refers background in this paper
...Topological representation captures the environment accessibility properties in a graph structure and provides a first level of abstraction allowing complex navigation tasks in large scale environments [21]....
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154 citations
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Frequently Asked Questions (12)
Q2. What are the future works mentioned in the paper "Appearance-based segmentation of indoors/outdoors sequences of spherical views" ?
For future work, the authors plan to improve their algorithm robustness to illumination condition following [ 6 ] and its rotation independence. De-rotation mechanism can be applied as rotations can be estimated from spectra.
Q3. What is the way to detect change-points?
The segmentation algorithm relies on an efficient change-point detection based on multi-hypothesis testing and allowing constant time computation.
Q4. What is the purpose of the algorithm?
In a longer term, the segmentation algorithm could be coupled with a loop closure detection algorithm in orderto improve change-point localization stability and with a semantic level by adding place classification and labelling.
Q5. What is the meaning of spherical harmonics?
Pml corresponds to the associated Legendre polynomials with x ∈ [−1, 1] such that:Pml (x) = (−1)m(1− x2)m/22ll!dl+mdxl+m (x2 − 1)l (3)Every function defined on the sphere surface can be decomposed in a sum of spherical harmonics as follows:f = ∑l∈N∑|m|≤lfml Y m l (4)The fml coefficients are obtained from a function f by:fml =∫η∈S2 f(η)Y ml (η)dη (5)If fml = 0 for all l > L, f is said to be band limited with a bandwidth L. The coefficients set fml is called the spherical Fourier transform or the spectrum of f .
Q6. What is the description of a place?
As descriptors are based on appearance frequencies, when the robot approaches walls, frequencies become lower and a new topological place is defined.
Q7. What is the spherical harmonics spectrum code?
the spherical harmonics spectrum code is highly parallelizable and might take great advantage of a C/C++ parallel implementation.
Q8. What is the size of the sliding window?
Considering the density function estimation constraints aforementioned, the sliding window has to be sufficiently large for a correct estimation.
Q9. What is the density function for each hypothesis?
Let’s assume the density functions under each hypothesis, i.e. f0 and f1, follow a multivariate normal distribution:f0 ∼ N (µ0,Σ0 f1 ∼ N (µ1,Σ1) (10)As each hypothesis is characteristic of one topological place, density functions characterize the structural parameters of topological places.
Q10. What is the definition of spherical harmonics?
Spherical harmonics being a frequency description of the spherical image, the authors propose to directly use the spectrum as a structure descriptor.
Q11. How long does the spherical harmonics spectrum computation take?
Spherical harmonics spectrum computation requires 290ms using the implementation described above (the sphere is sampled with 62500 samples uniformly distributed).
Q12. What is the frequency information of the spherical image?
Frequency information corresponds to band number l and orientation information to parameter m (the higher l is, the higher the frequency is, see fig.