Aerial imagery, including that from unmanned aerial vehicles (UAVs), has become increasingly popular. Its advantages, such as high spatial resolution, low cost, and ready availability, provide numerous potential applications [1,2,3]. Compared with low or median spatial resolution images, aerial images often have very high spatial resolution (VHSR). This provides more details of the earth surface, including the shape, structure, size, and texture of ground targets, and even topology and thematic information among targets. Therefore, a VHSR image is useful for investigating urban environments, target extraction, and urban land-cover mapping [4,5,6,7]. However, the higher resolution does not necessarily produce greater classification accuracies; VHSR image classification poses a challenge in practical application . This is because if the spatial resolution is very fine, then the classification could not be improved anymore because of the within-class variability in spectral values. To conquer this problem, spatial feature extraction and complementing with spectral features are known to be important technique in VHSR image classification .
Spatial feature extraction is aimed at describing the shape, structure, and size of a target on the earth surface. However, the spatial arrangement of the ground targets is complex and uncertain. Many researchers have proposed threshold-based approaches to extract spatial features and improve the performance of VHSR image classification. For example, Han et al. considered the shape and size of a homogeneous area, selecting suitable spatial features using parameters . Zhang et al. discussed a multiple shape feature set that can characterize the target using different points to enhance classification accuracy . However, an “optimal” threshold for a given image cannot be determined until a series of experiments has been carried out, which is very time-consuming. Although such a threshold can be selected by experiment, one cannot know whether it is indeed the best for all images. Furthermore, such a single optimal threshold may not handle the various shapes in all image cases.
Besides threshold-based extension methods, a mathematical model is an effective means to treat contextual information for extracting spatial features. For example, Moser et al. extracted spatial-contextual information using the Markov random field (MRF) . There is extensive literature on the use of MRF in VHSR image classification, such as [13,14,15]. Morphological profiles (MPs) represent another powerful tool for spatial feature extraction . The structural element (SE) is crucial to morphological operations, so MPs have been extended in size and shape by many researchers [9,17]. Furthermore, MP attributes have been exploited for describing spatial features of VHSR images [18,19,20]. Among these methods, contextual information within a “window” around a central pixel is simulated and a mathematical model extracted, such as the MRF or MPs. However, the main limitations of considering a set of neighbors using a regular window are the following: (i) The regular neighborhood may not cover the various shapes of different targets in the varying classes, or even different targets within a single class; (ii) although extension of the MP in size or shape can improve the classification performance, it is still inadequate to fit the various shapes and sizes of ground targets in an image scene. Therefore, the adaptive ability of a spatial feature extraction approach should be studied extensively. Ideally, spatial feature extraction should be driven by the image data itself.
In recent decades, many literature works have revealed that image object-based image analysis was effective for that classification [21,22]. An image object is a group pixel set with similar spectral values, such that the object has homogeneous spectra. Compared with pixel-based methods, the object-based approach has two advantages: (i) Image objects have more usable features (e.g., shape, size and texture) than a single pixel; (ii) because the processing unit is improved from pixel to object, much “salt and pepper” noise can be smoothed in the classification results. For example, Zhao et al. proposed an algorithm integrating spectral, spatial contextual, and spatial location cues within a condition random field framework to improve the performance of VHSR image classification . Zhang et al. proposed an object-based spatial feature called object correlative index (OCI) to improve land-cover classification . Most of image object-based classification methods rely on the performance of segmentation . However, the scale parameter of multi-resolution segmentation is difficult to determine . In the present work, we integrated an image raster and its corresponding segment vector to use topological relationships and geographic characteristics, with the aim of extracting VHSR image spatial features automatically.
The proposed approach is based on two simple assumptions: (i) Objects making up a target are not only spatially continuous but are also more homogeneous in spectra than objects not belonging to the same target; (ii) objects from one target usually have very similar auto-correlation. As shown in Figure 1, objects comprising a ground target appear spectrally very similar, and are continuous in the spatial domain. Based on this observation, Tobler’s First Law of Geography (TFL) of geographic and topologic relationships of an object is used to constrain the extension for exploring the target region. One advantage of this combination is that it can better model the spatial arrangement of a target and effectively detect the target regardless of its shape or size (e.g., the rectangular or “L” shaped building or linear road in Figure 1). For the second assumption above (ii), Moran’s Index (MI) is typically used to quantitatively measure auto-correlation of the pixels for an object. Then, objects making up a target with similar (homonymous) MI are used to constrain the extension. In other words, the extension of a region for an uncertain target should be driven by the TFL of geography and the target itself, rather than parameter constraints. Experimental results demonstrate outstanding classification accuracy performance of the proposed feature extraction method. This means that the two basic assumptions based on observation of the ground target’s geography are very useful in feature extraction of VHSR aerial imagery.
Contextual information of remote sensing imagery has been studied extensively and TFL has been widely applied in the field of geographic information systems (GIS). However, to the best of our knowledge, few approaches have been developed based on the TFL of geography for VHSR image classification in an object-manner. The present study proves that GIS spatial analysis can be used effectively for spatial feature extraction of VHSR images.
When an image is processed by multi-scale segmentation, the topological relationship between a central object and surrounding objects becomes more complex, unlike a central pixel and its neighboring pixels (e.g., 4-connectivity or 8-connectivity). Another contribution of this study is its extension strategy based on topology and spectral feature constraints, which is adaptive and improves modeling of the shape and size of an uncertain target.
Besides the segmentation, the progress of feature extraction is automatic, and no parameter adjustment is necessary during its application to classification. This opens up the possibility of widespread practical application to remote sensing imagery.
The remainder of this paper is organized as follows. In Section 2, TFL of geography is reviewed. In Section 3, the proposed feature extraction method is described. An experimental description is given in Section 4 and conclusions are given in Section 5.
2. Review of Tobler’s First Law of Geography
Here, we briefly review TFL. According to Waldo Tobler, the first law of geography is that “everything is related to everything else, but near things are more related than distant things” . It is evident from this law that it was largely ignored and the quantitative revolution declined, but it gained prominence with the growth of GIS. Despite notable exceptions, it is hard to imagine a world in which the law is not true, and it provides a very useful principle for analyzing earth surface information . The widespread application of geography today accommodates a variety of perspectives on the significance of this law [29,30]. Remote sensing imagery is obtained based on the radiance of specific source targets on the ground surface. Therefore, when an image is segmented into objects, those objects are related in the spatial and spectral domains. Thus, TFL of geography is applicable to image analysis.
Here, b is the band index of the image and n is the total number of bands. N is the total number of pixels within the object. is a pixel value of band b within o. is an element of a matrix of spatial weights; if xi and xj are neighbors, , otherwise . is the mean of pixels within o.
The constraint-rule on the extension around a central object is analyzed further in Section 3. In particular, we had two objectives: (i) TFL of geography is introduced for spatial feature extraction of a VHSR image, and its feasibility investigated; (ii) to reduce the classification algorithm’s data dependence and expand application of the VHSR image, we advance a “rule-constraint” automatic feature extraction method based on TFL of geography, instead of the traditional parameter-based feature extraction approach. One important difference between TFL in our study and spatial contextual information related in existing approaches is that TFL is adopted as a “relaxing rule” in the description of neighboring information, while many existing approaches describe the spatial contextual information in a rigorous manner. In addition, the relaxing rule in our study is driven adaptively by the contextual information rather than by a preset parameter. Details of our proposed methods are presented in Section 3.
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