| A spatial pattern is an important geometrical feature of a land surface ecosystembecause it affects the ecological process and function; therefore, the analyses ofspatial patterns have been extensively conducted in geosciences fields. As animportant tool for earth observation, remote sensing technology provides a wealth ofspatial data sources; the recognition of spatial patterns is one of the essential tasks invarious applications of remotely sensed images, and recently, the generation of a largenumber of high spatial resolution images provides a better opportunity for perceivingmore detailed spatial patterns. Numerous effective approaches have been developed tocharacterize and quantify the spatial patterns in remote sensing images, of whichsemi-variograms and average local variance(ALV) functions are most commonly used.Both semi-variograms and ALV functions directiy establish the relationship betweenthe size of objects in the scene and spatial resolution of remote sensing image, andprovide an indication of the spatial patterns in the investigated area.Studing the fundamentals of detecting spatial pattern in remote sensing images,which contribute to improve the understanding of the detecting spatial patternmethods and enable the effective improvement of their detection capacity in practicalapplication. However, the research on fundamentals of semi-variograms and ALVfunctions which are used to detect spatial pattern in remote sensing images arerelatively less; and previous studies the fundamentals of the two methods involved anexceedingly limited number of object sizes and window sizes rather than using theirsequences, which possibly resulted in the incomplete elucidation of the capacity of thetwo approaches in spatial pattern detection. To solve the above problems, firstly, aseries of one-dimensional and two-dimensional synthetic images representing various regular spatial patterns were constructed, and continuously change the relatedparameters for calculating ALV and semi-variograms, in order to explore theircapability for detecting spatial pattern; secondly, a series random of one-dimensionaland two-dimensional discrete synthetic images with various spatial patterns andshapes were constructed, to future study their capability for detecting spatial pattern;finally, several real remote sensing images with various spatial patterns were used tofuture studies and verifies their capability for detecting spatial pattern. Through amore systematic and in-depth research the fundamentals and capability of the twomethod for detecting spatial pattern, get several aspects of research conclusion asfollowing:(1) Detecting the size of objectsThe peak position of the ALV graph does not vary as a function of the size of theobject, due to their complex relationship when the ALV method is used to detect thesize of objects in regular images; the number and position of the ALV graph arecontrolled by the scene period. Through the peak position of the ALV graph isdifficult to determine the size of objects, and also can’t get the range of objects sizewhen the ALV method is used to detect spatial patterns in random and real images.The object size and background size can be detected by the inflection point ofsemi-variograms when the semi-variograms method is used to detect the spatialpatterns size in regular images; and the scene period does not have an impact on theresult. However, the inflection point of semi-variograms may stand for the object sizeor background size which need to introduce the mean of images to accurate judgment.But, through the inflection point of semi-variograms is difficult to determine the sizeof objects when the semi-variograms method is used to detect spatial patterns inrandom and real images.(2) Detecting the size of scene periodThe size of period is closely linked with the position of key trough in ALV graph,and can better be detected by the position of key trough in ALV graph when the ALVmethod is used to detect the size of period in regular images.The size of period can better be detected by the position of trough in semi-variograms when the semi-variograms method is used to detect the size ofperiod in regular images.(3) Accurate detection the size of objects for regular patternsFor the regular patterns remote sensing images, an new statistics model on theparameters of the exponent formulas containing the size of object is proposed basis onthe theory that the position of key trough in ALV graph can detect the size of period,which can be used to predict the size of object in the regular scene image andovercomes the limitation of the traditional ALV method for detecting the objects sizein remote sensing images.(4) Effection of window sizeWhatever the size of period is prime number or composite number, an increase inwindow size influence the peak position and the peak number, but does not have animpact on the position of the key trough when the ALV method is used to detect thespatial patterns in regular images. The peak position of ALV graph drifts toward theleft as increase window size when the ALV method is used to detect the spatialpatterns in random and real images.An increase in window size influence the inflection point position and theinflection point number of semi-variograms, and the inflection point ofsemi-variogram will disappear, when the semi-variograms method is used to detectthe spatial patterns in regular images. The inflection point position ofsemi-variograms drifts toward the right as increase window size when thesemi-variograms method is used to detect the spatial patterns in random and realimages.(5) Effection of iamges extentIf the peak position and key trough both appear in ALV graph, the extent ofimages, at least, has2×W×P (W is window size，P is the period of scene) pixels whenthe ALV method is used to detect the spatial patterns in regular images.The extent of images, at least, is twofold of the scene period that can detect theobject size and background size when the lag of semi-variograms method is one pixelused to detect the spatial patterns in regular images. For random and real images, spatial patterns and images extent are dependencethat different image extent contains various patterns size; therefor, the extent ofrandom and real images will impact the peak position of ALV graph and the inflectionpoint position of semi-variograms. |
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