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 CS225B Kurt Konolige

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 CS225B Kurt Konolige

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 CS225B Kurt Konolige

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 CS225B Kurt Konolige

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 6/2/2019 CS225B Kurt Konolige

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 6/2/2019 CS225B Kurt Konolige

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 6/2/2019 CS225B Kurt Konolige

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 6/2/2019 CS225B Kurt Konolige

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? 6/2/2019 CS225B Kurt Konolige

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 6/2/2019 CS225B Kurt Konolige

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 CS225B Kurt Konolige

Techniques: Incremental Line Fitting From T. Darrell course notes 6/2/2019 CS225B Kurt Konolige