Model estimation and data fitting needs arise in all sorts of computer vision problems. Here, we show some examples for

  • Constrained least squares fitting
    As an example, we present results for finding a quadratic spline from noisy point samples. Here, we solve the data fitting problem using equality and inequality constraints in addition to the data fitting constraints.
  • Multiple model estimation with unknown model number
    As an example, we show the results for finding an unknown number of lines from a set of distributed 2d points.


Constrained Least Squares Fitting



Each colored curve below represents a quadratic polynomial. By using a combination of polynomials defined over different intervals of the input data, a smooth spline is computed. Smoothness is enforced by solving the problem with the equality constraints on the end-points of the polynomials i.e. each polynomial and its derivative evaluate to the same value with the next polynomial at the interval boundary end-points.

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Multiple Model Fitting with Unknown Model Number



The 2d point sets on the left contain an unknown number of linear models in them. Our solution (shown on the right) finds the set of lines and the points belonging to these lines automatically without the need for the user to enter any input.

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