Spatial ARMA models and its applications to image filtering

Bustos, Oscar H.; Ojeda, Silvia María; Vallejos, Ronny

doi:10.1214/08-bjps019

Cited by 27 publications

(15 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The ability to account for longer range correlations is important also for forecasting future changes in the interaction effect. The ARI(MA) models extend in a rather straightforward way to the spatial domain (e.g …”

Section: Extensions To the Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Bayesian age–period–cohort models with versatile interactions and long‐term predictions: mortality and population in Finland 1878–2050

Havulinna

2013

Statistics in Medicine

View full text Add to dashboard Cite

Age-period-cohort (APC) models are widely used for studying time trends of disease incidence or mortality. Model identifiability has become less of a problem with Bayesian APC models. These models are usually based on random walk (RW1, RW2) smoothing priors. For long and complex time series and for long predicted periods, these models as such may not be adequate. We present two extensions for the APC models. First, we introduce flexible interactions between the age, period and cohort effects based on a two-dimensional conditional autoregressive smoothing prior on the age/period plane. Our second extension uses autoregressive integrated (ARI) models to provide reasonable long-term predictions. To illustrate the utility of our model framework, we provide stochastic predictions for the Finnish male and female population, in 2010-2050. For that, we first study and forecast all-cause male and female mortality in Finland, 1878-2050, showing that using an interaction term is needed for fitting and interpreting the observed data. We then provide population predictions using a cohort component model, which also requires predictions for fertility and migration. As our main conclusion, ARI models have better properties for predictions than the simple RW models do, but mixing these prediction models with RW1 or RW2 smoothing priors for observed periods leads to a model that is not fully consistent. Further research with our model framework will concentrate on using a more consistent model for smoothing and prediction, such as autoregressive integrated moving average models with state-space methods or Gaussian process priors.

show abstract

Section: Extensions To the Modelsmentioning

confidence: 99%

“…The ARI(MA) models extend in a rather straightforward way to the spatial domain (e.g. [24]). The spatial ARI model for the interaction effect pa is where pa is optionally differenced.…”

Section: Spatial Integrated Autoregressive Model For Predicting the Imentioning

confidence: 99%

Bayesian age–period–cohort models with versatile interactions and long‐term predictions: mortality and population in Finland 1878–2050

Havulinna

2013

Statistics in Medicine

View full text Add to dashboard Cite

show abstract

“…Here, we consider other prediction windows to observe the effect on the performance of Algorithm 2. A description of the most commonly used prediction windows in statistical image processing is in Bustos et al, (2009a). A brief description of the strongly causal prediction windows is given below.…”

Section: Improving the Segmentation Algorithmmentioning

confidence: 99%

Image Segmentation and Time Series Clustering Based on Spatial and Temporal ARMA Processes

Vallejos¹,

Ojeda²

2012

Advances in Image Segmentation

Self Cite

View full text Add to dashboard Cite

“…In this sense the spatial autoregressive model (AR-2D model) has been extensively used to represent images ( [3], [14]) due to its two main properties. First, simulation experiments have shown that this model is adequate to represent a diversity of real scenarios ( [4]). Second, the AR-2D model does not require a large number of parameters to represent different real scenarios (parsimony) ( [4]).…”

Section: Introductionmentioning

confidence: 99%

“…First, simulation experiments have shown that this model is adequate to represent a diversity of real scenarios ( [4]). Second, the AR-2D model does not require a large number of parameters to represent different real scenarios (parsimony) ( [4]). In particular, the first-order AR-2D model is able to represent a wide range of texture images, as is shown in Figure 1; the image (a) have been generated by a first-order AR-2D model with three parameters, while images (b), (c), (d) and (e) have been generated by a model of the same type with two parameters.…”

Section: Introductionmentioning

confidence: 99%

A New Algorithm to Represent Texture Images

Ojeda¹,

Britos²

2013

IJACSA

View full text Add to dashboard Cite

Abstract-In recent times the spatial autoregressive models have been extensively used to represent images. In this paper we propose an algorithm to represent and reproduce texture images based on the estimation of spatial autoregressive processes. The image intensity is locally modeled by a first spatial autoregressive model with support in a strongly causal prediction region on the plane. A basic criteria to quantify similarity between two images is used to locally select this region among four different possibilities, corresponding to the four strongly causal regions on the plane. Two global image similarity measures are used to evaluate the performance of our proposal.

show abstract

Spatial ARMA models and its applications to image filtering

Cited by 27 publications

References 45 publications

Bayesian age–period–cohort models with versatile interactions and long‐term predictions: mortality and population in Finland 1878–2050

Bayesian age–period–cohort models with versatile interactions and long‐term predictions: mortality and population in Finland 1878–2050

Image Segmentation and Time Series Clustering Based on Spatial and Temporal ARMA Processes

A New Algorithm to Represent Texture Images

Contact Info

Product

Resources

About