Affiliations: [a] Laboratorio de Investigación en Matemática Aplicada al Control, Universidad Nacional de Córdoba, Córdoba, Argentina | [b] Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Argentina and CIEM-CONICET, Córdoba, Argentina | [c] Instituto de Automática, Universidad Nacional de San Juan, Argentina and CONICET, Argentina
Correspondence:
[*]
Corresponding author: Josef Baumgartner, Laboratorio de Investigación en Matemática Aplicada al Control, UNC, Córdoba, Vélez Sarsfield 1611, X5016GCA Córdoba, Argentina. E-mail:[email protected]
Abstract: Image segmentation is one of the fundamental problems in computer vision. In this work, we present a new segmentation algorithm that is based on the theory of two-dimensional hidden Markov models (2D-HMM). Unlike most 2D-HMM approaches we do not apply the Viterbi algorithm; instead we present a computationally efficient algorithm that propagates the state probabilities through the image. Our algorithm, called Complete Enumeration Iteration (CEP), is flexible in the sense that it allows the use of different probability distributions as emission probabilities. Not only do we compare the performance of different probability functions plugged into our framework but also propose three methods to update the distributions of each state ``online'' during the segmentation process. We compare our algorithm with a 2D-HMM standard algorithm and Iterated Conditional Modes (ICM) using real world images like a radiography or a satellite image as well as synthetic images. The experimental results are evaluated by the kappa coefficient (\widehat{κ}). In those cases where the average \widehat{κ} coefficient is higher than 0.7 we observe an average relative improvement of 8% of CEP with respect to the benchmark algorithms. For all other segmentation tasks CEP shows no significant improvement. Besides that, we demonstrate how the choice of the emission probability can have great influence on the segmentation results. Surprisingly, we observe that the normal distribution is an appropriate density function for many segmentation tasks.
Keywords: Image segmentation, hidden Markov models, viterbi training, probability density function, kappa coefficient
