Minimizing sparse high-order energies by submodular vertex-cover
В данной работе рассматриваются модели формы объектов на изображении: бинарная и многоклассовая модели Больцмана. Предлагается новый алгоритм обучения многоклассовой модели формы Больцмана, для применения которого достаточно неполной разметки данных, а именно: бинарной разметки и задания семян, указывающих приближенное расположение частей объектов.
The Shape Boltzmann Machine (SBM) and its multilabel version MSBM have been recently introduced as deep generative models that capture the variations of an object shape. While being more flexible MSBM requires datasets with labeled parts of the objects for training. In the paper we present an algorithm for training MSBM using binary masks of objects and the seeds which approximately correspond to the locations of objects parts. The latter can be obtained from part-based detectors in an unsupervised manner. We derive a latent variable model and an EM-like training procedure for adjusting the weights of MSBM using a deep learning framework. We show that the model trained by our method outperforms SBM in the tasks related to binary shapes and is very close to the original MSBM in terms of quality of multilabel shapes.
In this paper we address the problem of finding the most probable state of a discrete Markov random field (MRF), also known as the MRF energy minimization problem. The task is known to be NP-hard in general and its practical importance motivates numerous approximate algorithms. We propose a submodular relaxation approach (SMR) based on a Lagrangian relaxation of the initial problem. Unlike the dual decomposition approach of Komodakis et al., 2011 SMR does not decompose the graph structure of the initial problem but constructs a submodular energy that is minimized within the Lagrangian relaxation. Our approach is applicable to both pairwise and high-order MRFs and allows to take into account global potentials of certain types. We study theoretical properties of the proposed approach and evaluate it experimentally.