Discriminative Learning of Markov Random Fields for Segmentation of 3D Scan Data

Abstract

We address the problem of segmenting 3D scan data into objects or object classes.

Cutting-plane training of structural SVMs

“…Intuitively, one can think of f w (x, y) as a compatibility function that measures how well the output y matches the given input x. The flexibility in designing Ψ allows us to employ SVMs to learn models for problems as diverse as natural language parsing Tsochantaridis et al 2004), protein sequence alignment (Yu et al 2007), learning ranking functions that optimize IR performance measures (Yue et al 2007), and segmenting images (Anguelov et al 2005).…”

“…Existing algorithm fall into two groups. The first group of algorithms relies on an elegant polynomial-size reformulation of the training problem (Taskar et al 2003;Anguelov et al 2005), which is possible for the special case of margin-rescaling (Tsochantaridis et al 2005) with linearly decomposable loss. These smaller QPs can then be solved, for example, with general-purpose optimization methods (Anguelov et al 2005) or decomposition methods similar to SMO (Taskar et al 2003;Platt 1999).…”

“…The first group of algorithms relies on an elegant polynomial-size reformulation of the training problem (Taskar et al 2003;Anguelov et al 2005), which is possible for the special case of margin-rescaling (Tsochantaridis et al 2005) with linearly decomposable loss. These smaller QPs can then be solved, for example, with general-purpose optimization methods (Anguelov et al 2005) or decomposition methods similar to SMO (Taskar et al 2003;Platt 1999). Unfortunately, decomposition methods are known to scale super-linearly with the number of examples (Platt 1999;Joachims 1999), and so do general-purpose optimizers, since they do not exploit the special structure of this optimization problem.…”

Graph Cut Based Point-Cloud Segmentation for Polygonal Reconstruction

“…They build a weighted graph, pre-segment it with thresholding and then the graph cut is applied on the wrongly presegmented parts, based on user will. Anguelov et al applied the Markov Random Fields for point-cloud and range data segmentation in [17] where the object segmentation is based on local surface features. Trained Markov Random Fields can be solved through graph cut.…”

Optimal Weights for Convex Functionals in Medical Image Segmentation

“…The first set is based on recent advances in maximum margin estimation, wherein the parameters of the objective function are sought such that the highest scoring structures (in our case segmentations) are as close as possible to the ground truth [10,11,12,13]. However, in addition to being limited to combinatorial objective functions rather than continuous ones, these methods propose a fixed set of parameters for novel samples (in our case images), whereas we follow the direction of [9] using geodesic interpolation to infer the optimal parameters on a per-image basis.…”