Unsupervised amplitude and texture based classification of SAR images with multinomial latent model

We combine both amplitude and texture statistics of the Synthetic Aperture Radar (SAR) images for classification purpose. We use Nakagami density to model the class amplitudes and a non-Gaussian Markov Random Field (MRF) texture model with t-distributed regression error to model the textures of the classes. A non-stationary Multinomial Logistic (MnL) latent class label model is used as a mixture density to obtain spatially smooth class segments. The Classification Expectation-Maximization (CEM) algorithm is performed to estimate the class parameters and to classify the pixels. We resort to Integrated Classification Likelihood (ICL) criterion to determine the number of classes in the model. We obtained some classification results of water, land and urban areas in both supervised and unsupervised cases on TerraSAR-X, as well as COSMO-SkyMed data

Unsupervised amplitude and texture classification of SAR images with multinomial latent model

International audienceWe combine both amplitude and texture statistics of the Synthetic Aperture Radar (SAR) images for modelbased classification purpose. In a finite mixture model, we bring together the Nakagami densities to model the class amplitudes and a 2D Auto-Regressive texture model with t-distributed regression error to model the textures of the classes. A nonstationary Multinomial Logistic (MnL) latent class label model is used as a mixture density to obtain spatially smooth class segments. The Classification Expectation-Maximization (CEM) algorithm is performed to estimate the class parameters and to classify the pixels. We resort to Integrated Classification Likelihood (ICL) criterion to determine the number of classes in the model. We present our results on the classification of the land covers obtained in both supervised and unsupervised cases processing TerraSAR-X, as well as COSMO-SkyMed data

The General Consistent Labeling (or Constraint Satisfaction) Problem

https://deepblue.lib.umich.edu/bitstream/2027.42/154162/1/39015099114897.pd

Generating Preferential Attachment Graphs via a P\'olya Urn with Expanding Colors

We introduce a novel preferential attachment model using the draw variables of a modified P\'olya urn with an expanding number of colors, notably capable of modeling influential opinions (in terms of vertices of high degree) as the graph evolves. Similar to the Barab\'asi-Albert model, the generated graph grows in size by one vertex at each time instance; in contrast however, each vertex of the graph is uniquely characterized by a color, which is represented by a ball color in the P\'olya urn. More specifically at each time step, we draw a ball from the urn and return it to the urn along with a number (potentially time-varying and non-integer) of reinforcing balls of the same color; we also add another ball of a new color to the urn. We then construct an edge between the new vertex (corresponding to the new color) and the existing vertex whose color ball is drawn. Using color-coded vertices in conjunction with the time-varying reinforcing parameter allows for vertices added (born) later in the process to potentially attain a high degree in a way that is not captured in the Barab\'asi-Albert model. We study the degree count of the vertices by analyzing the draw vectors of the underlying stochastic process. In particular, we establish the probability distribution of the random variable counting the number of draws of a given color which determines the degree of the vertex corresponding to that color in the graph. We further provide simulation results presenting a comparison between our model and the Barab\'asi-Albert network.Comment: 21 pages, 6 figure