پيش گويي فضايي با مدل هاي اتورگرسيو يك طرفه در فضاي دو بعدي آ

Spatial Prediction By Using Unilateral Autoregressive Models In Two-Dimensional Space

ﭼﮑﯿﺪه: ﯾﮑﯽ از ﻣﻮﺿﻮﻋﺎت ﻣﻬﻢ در ﺗﺤﻠﯿﻞ داده ﻫﺎي ﻓﻀﺎﯾﯽ، ﭘﯿﺶ ﮔﻮﯾﯽ ﻣﻘﺪار ﻧﺎﻣﻌﻠﻮم ﮐﻤﯿﺖ ﻣﻮرد ﻣﻄﺎﻟﻌﻪ در ﻣﻮﻗﻌﯿﺖ ﻫﺎي دﻟﺨﻮاه ﺑﺮ اﺳﺎس ﯾﮑﯽ از ﻣﺪل ﻫﺎي ﻓﻀﺎﯾﯽ ﻣﺎﻧﻨﺪ اﺗﻮرﮔﺮﺳﯿﻮ ﻓﻀﺎﯾﯽ ﯾﮏ ﻃﺮﻓﻪ، اﺗﻮرﮔﺮﺳﯿﻮ ﺷﺮﻃﯽ و ﻣﯿﺎﻧﮕﯿﻦ ﻣﺘﺤﺮك اﺳﺖ. در اﯾﻦ ﻣﻘﺎﻟﻪ اﺑﺘﺪا ﭘﺎراﻣﺘﺮﻫﺎي ﻣﺪل )2, 1(SAR را ﺑﻪ روش ﻣﺎﮐﺴﯿﻤﻢ درﺳﺘﻨﻤﺎﯾﯽ ﺑﺮآورد ﮐﺮده ﺳﭙﺲ ﻓﺮﻣﻮل ﻫﺎﯾﯽ ﺑﺮاي ﭘﯿﺶ ﮔﻮﯾﯽ درون ﻗﻠﻤﺮو داده ﻫﺎ )درون ﯾﺎﺑﯽ( و ﺧﺎرج ﻗﻠﻤﺮو داده ﻫﺎ )ﺑﺮون ﯾﺎﺑﯽ( ﺑﻪ دﺳﺖ آورده ﻣﯽ ﺷﻮد. ﺳﭙﺲ ﮐﺎرﺑﺮد و ﮐﺎراﯾﯽ روش ﻫﺎي اراﺋﻪ ﺷﺪه در ﻗﺎﻟﺐ ﯾﮏ ﻣﺜﺎل ﻣﺮﺑﻮط ﺑﻪ ﭘﺮدازش ﺗﺼﻮﯾﺮ ﻧﺸﺎن داده ﺧﻮاﻫﺪ ﺷﺪ.

Prediction of spatial variability is one of the most important issues in the analysis of spatial data. So predictions are usually made by assuming that the data follow a spatial model. In General, the spatial models are the spatial autoregressive (SAR), the conditional autoregressive and the moving average models. In this paper, we estimated parameter of SAR(2,1) model by using maximum likelihood and obtained formulas for predicting in SAR models, including the prediction within the data (interpolation) and outside the data (extrapolation). Finally, we evaluate the prediction methods by using image processing data.