1. Introduction to Sensor Interpretation
What is “sensor interpretation”?
- abstraction of high-dimensional input spaces to low-dimensional output spaces
- interpreting reduced data according to the task at hand
Why interpret sensors?
- working with large datasets is expensive
- smoothing and filtering based on models can yield better results in applications
From Ziegler et al., 3D Reconstruction Using Labeled Image Regions
6/2/2019
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2. A General View of Sensor Interpretation
Measurements
Features
[filtering, data reduction]
Model Fit
[robust techniques, outlier rejection]
Interpretation
Features
Dimensionality reduction of the data
Models
A model is a mathematical description of the abstract feature, controlled by a few parameters
Interpretation
How can the modeled data be interpreted to perform a task?
6/2/2019
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3. Some Issues Models Sensor Noise
A model is a mathematical description of the abstract feature, controlled by a few parameters
Sensor Noise
Noise is the deviation of a sensor reading from its ideal value
Noise complicates the process of feature extraction, and makes probabilistic techniques useful
Graphs from Guo, A Multiple-Line Fitting Algorithm without Initialization
6/2/2019
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4. Some Issues Segmentation Outliers / Data association
What is the important part or parts of a set of sensor readings?
Figure/ground distinction [Edgar Rubin]
Outliers / Data association
Some readings are not associated with the feature at all, and do not correspond to normal noise values
[Roger Shepard]
Graph from Guo, A Multiple-Line Fitting Algorithm without Initialization
6/2/2019
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5. Techniques: Maximum Likelihood
Maximum Likelihood Method [Linear Regression]
Measurement function
Independent measurements zi with value
Gaussian distribution of error, with the same variance for each zi
THEN –
maxx p(x|z) is given by
Line parameters: slope, intercept
Measurement equation:
s,i x
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6. Techniques: Maximum Likelihood
Maximum Likelihood Issues
Which model? - some are better than others
What is a good measure of fit?
How many line segments?
Outliers – Gaussian assumption means outliers pull a lot of weight
Solutions are in robust statistics
Ignore high residuals
Least Median of Squares [Rousseeuw]
Consensus estimators
Unequal Variance
Some measurements should count more more than others
Mahalanobis distance:
s,i x
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7. Techniques: Hough Transform
Slope/intercept parameterization of a line
A point in (a,d) represents a line in (x,y)
For a give point (x,y), there is a family of lines going through the point – a curve in (a,d)
From T. Darrell course notes
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8. Techniques: Hough Transform
Issues
Representing curves in (a,d) – typically use a grid of cells
For each point in (x,y), increment the count in corresponding cells
Find loci
Noise, resolution, and computation are problems
From T. Darrell course notes
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9. Techniques: RANSAC [Fischler and Bolles]
RANdom SAmple Consensus
Uses consensus to determine data association
Uses random sampling to find “seeds” for consensus
Robust to outliers
Can find multiple features
How many pairs must we pick before we find a good line?
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10. Techniques: RANSAC [Fischler and Bolles]
Algorithm
Function f(x) = y for finding a model y from a set of data points x of size n (e.g., in the case of lines, two or more points)
Choose a random set x
Find all inliers to model y
Accept if inliers > threshold (maybe replace previous model, or add to models if using multiple models)
Iterate for some number k
How many pairs must we pick before we find a good line?
z is the probability of only bad picks
k is chosen based on z
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11. Techniques: Incremental/Recursive Line Fitting
Order points along the curve
Start with a straight line connecting the first and last points
Find point with max distance
Split and apply algorithm to each segment
Incremental Line Fitting
Order points along the curve
Add next few points to a new line
Fit line and check residual
If residual is good, add next point and re-fit
If residual is bad, declare line done and start a new line
6/2/2019
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12. Techniques: Incremental Line Fitting
From T. Darrell course notes
6/2/2019
CS225B Kurt Konolige