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.

### 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.