  We propose a general formulation, called Multi-X, for multi-class
multi-instance model fitting - the problem of interpreting the input data as a
mixture of noisy observations originating from multiple instances of multiple
classes. We extend the commonly used alpha-expansion-based technique with a new
move in the label space. The move replaces a set of labels with the
corresponding density mode in the model parameter domain, thus achieving fast
and robust optimization. Key optimization parameters like the bandwidth of the
mode seeking are set automatically within the algorithm. Considering that a
group of outliers may form spatially coherent structures in the data, we
propose a cross-validation-based technique removing statistically insignificant
instances. Multi-X outperforms significantly the state-of-the-art on publicly
available datasets for diverse problems: multiple plane and rigid motion
detection; motion segmentation; simultaneous plane and cylinder fitting; circle
and line fitting.
