SIZE-CONSTRAINED REGION MERGING: A NEW TOOL TO DERIVE BASIC LANDCOVER UNITS FROM REMOTE SENSING IMAGERY Guillermo Castilla IDR, Campus Universitario, 02071 Albacete, Spain, Email:
[email protected]
ABSTRACT Landcover maps typically represent the territory as a mosaic of contiguous units –polygons- that are assumed to correspond to geographic entities –like e.g. lakes, forests or villages-. They may also be viewed as representing a particular level of a landscape hierarchy where each polygon is a holon –an object made of subobjects and part of a superobject. The focal level portrayed in the map is distinguished from other levels by the average size of objects compounding it. Moreover, the focal level is bounded by the minimum size that objects of this level are supposed to have. Based on this framework, we have developed a segmentation method that defines a partition on a multiband image such that i) the mean size of segments is close to the one specified; ii) each segment exceeds the required minimum size; and iii) the internal homogeneity of segments is maximal given the size constraints. This paper briefly describes the method, focusing on its region merging stage. The most distinctive feature of the latter is that while the merging sequence is ordered by increasing dissimilarity as in conventional methods, there is no need to define a threshold on the dissimilarity measure between adjacent segments. Keywords: image segmentation, object-oriented image analysis, landcover mapping. 1.
INTRODUCTION
In the last decades, as a result of progress in Computing, Remote Sensing (RS) and Geographic Information Science, there has been a trend towards automated landcover mapping using digital classification. Nevertheless, the overall accuracy of the maps produced in this way is usually below the user’s requirements. Consequently most landcover mapping projects still rely to some extent on photointerpretation. Conventional classification methods treat each pixel as a sample measurement from a larger element (patch) made of a particular homogeneous material (landcover
class). The identification of the material is performed using the location of the sample in a feature space. Despite being commonplace, their output is usually considered unsatisfactory from an operational point of view, especially when the task is directed towards the maintenance of spatial databases within a Geographic Information System (GIS). The reason behind is that these methods ignore the fact that samples do not come separately as in a desktop spectrometer, they rather are knitted into an image full of spatial patterns. Besides, they cannot take advantage of the relational features used by photo-interpreters. Since the latter are too slow and scarce as to seize the huge amount of data regularly acquired by satellites, Earth Observation (EO) data are not used as frequently for natural resource monitoring and management as envisioned by the engineers who developed them [1]. This confronts space agencies and vendors with a serious problem. The former find difficult to justify expensive investment in EO programmes and desperately search for new users and applications. The latter sadly confirm one year after another that the pace of sales does not follow expectations. The response to such situation may take the form of a paradigm shift [2] that triggers new developments. In our context, it may be a shift from the above mentioned conventional approach to the object-oriented approach (OOA). The latter uses objects in addition to classes in order to model the landscape. Within OOA, an object represents an individual, unit, or entity, either real or abstract, with a well-defined role in the problem domain [3]. Vg a landscape object is a patch, defined as a discrete spatial unit having a certain minimum extension and differing from its surroundings in nature or appearance. Any given object is an instance of some particular class. Conversely, a class is a set of objects that share a common structure and a common behaviour. The class relations among objects are represented in ‘kind –of’ hierarchies (taxonomies) that provide inheritance, and structural relations among objects are represented in a ‘part-of’ hierarchies (partonomies) that provide encapsulation (information hiding) [3].
The OOA is especially suited for implementing a new paradigm in Landscape Ecology: the hierarchical patch dynamics [4], similar but more elaborated than the nested-hierarchical scene model already proposed in Remote Sensing [5]. Under this paradigm, the landscape is modelled as a hierarchical system having both vertical structure –composed of levels, and horizontal structure –consisting of patches or holons (wholes made of other wholes). The integration of each patch is such that the subunits compounding it (i.e. patches from the next lower level) interact more strongly or more frequently among them than with subunits of neighbouring patches. Hence, higher levels are characterized by slower and larger entities loosely integrated (e.g. a forest), whereas lower levels are characterized by faster and smaller entities (e.g. a tree) more tightly integrated than the former. Therefore, at different levels, a patch may be an entity ranging from the area covered by an isolated tree to an island continent. Patches from different levels may overlap in size, but the mean size of patches within each level must increase steadily with the level. Since there are no crisp distinctions between adjacent levels in the hierarchy, an arbitrary size threshold must be established for a given area to qualify as a patch of a certain level. Such threshold is analogous to the minimum mapping unit (MMU) used in cartography to impose the desired level of generalisation over the territory. There are three basic assumptions that, if true, justify the use of RS images to derive landcover maps under the hierarchical patch model [6]. First, image objects (segments) coincide with landscape objects (patches). Second, objects of the focal level having a size below a certain threshold (given e.g. by the MMU size) do not exist or can be neglected. And third, the likelihood of two adjacent image segments belonging to the same patch of the focal level increases with their radiometric similarity. Based on these premises, we have developed a segmentation method that defines a partition on a multiband image such that i) each segment exceeds the required minimum size; ii) the average size of segments within the partition is close to the required one; and iii) the internal homogeneity of segments is maximal given the size constraints. This partition is equivalent to a tessellation of the scene consisting of irregularly-shaped resolution cells of variable size. Each cell is a segment (a unitary region with no disjoint parts) that is different from its neighbours at least in one feature. Being their boundaries in a good agreement with the spatial variation in the image, segments may be viewed as image objects. In addition, each segment exceeds the size required for objects of the focal level, hence it can be classified as an instance of some type of object of that level. In contrast, the cells of a square grid have arbitrary boundaries and may have too small a size. Moreover, new attributes related to shape, topology (context) and heterogeneity can be derived for segments, while not for pixels.
Such partition, constructed as described below, is proposed as a baseline for an object-oriented classification of landcover. The latter may be conducted by means of a semantic net [7] that formulates knowledge about the objects of interest and their mutual relations. An example would be the Fractal Net Evolution Approach (FNEA) adopted by the eCognition software (http://www.definiens-imaging.com). FNEA describes complex image semantics within selforganizing hierarchical networks, in which the structure of each level is similar to the one of the others (hence the ‘fractal’ adjective). Objects derived from the input image change their states (structure and meaning) stepwise according to contextual influences and converge to a semantically coherent hierarchical arrangement through alternating procedures of segmentation and classification (hence the name ‘evolution’). 2.
BACKGROUND
There are a number of major contributions that have inspired in one way or another the Size-Constrained Region Merging (SCRM) algorithm. The first one is the stepwise optimisation algorithm of Beaulieu and Goldberg [8]. It begins by considering single pixels as the initial segments. At each iteration, the two adjacent segments that shows the highest degree of fitting are merged. In other words, the candidate pair merged at each pass is the one whose mergence produces the least increment in heterogeneity. Segments are merged gradually in this way until there is no candidate pair below a user-defined threshold. The final partition is optimal regarding the minimization of the heterogeneity criterion, but the procedure is too slow, since it allows only one mergence per pass (a strategy known as global mutual best fitting). Based on these authors’ work, Woodcock and Harward [5] introduced a faster algorithm that allows multiple mergences per pass and that included some size constraints. As these authors noted, the global threshold alone leads to inadequate results, since usually there is a great disparity in size of the output regions. Areas marked by coarse texture will consist of many small regions (often individual pixels), whereas smooth uniform areas will be segmented into large regions. As a result it is very unlikely that all the regions defined by a conventional segmentation method correspond to patches of the same hierarchic level. Hence the need for size constraints focusing on a certain hierarchic level. Therefore they supplemented their algorithm with some size constraints that prevented excessive growing in smooth areas and forced the development of segments exceeding the minimum required size in areas with high local variance.
Another way of tackling the uneven growth of segments between areas of smooth and coarse texture is to enable multiple mergences per pass, distributing the candidate pairs to be merged at each iteration as far as possible from each other over the image. This is the strategy followed by the segmentation algorithm [9] embedded in eCognition. In this way, it achieves a uniform growth of segments throughout the image, so that the final segments have all a similar size. Since a conservative (small) threshold permits fewer mergences than a greater one, the mean size of segments will grow with the value of the threshold. For this reason the threshold is a sort of scale parameter, although users have to find useful segmentation levels in a trial and error basis. Another particularity of eCognition’s segmentation is the optional inclusion of a form heterogeneity factor in the overall dissimilarity between two adjacent segments of size n1 and n2. The latter is measured as the change in heterogeneity produced by their eventual mergence, i.e. the difference hdiff (weighted by size) between the heterogeneity hm of the potential merger and the ones h1 and h2 of the segments: hdiff = (n1+n2)hm – (n1h1+ n2h2). The overall heterogeneity hi is a linear combination of radiometric variance and form heterogeneity (expressed e.g. by the ratio between factual edge length and the edge of a square with the same number of pixels than the segment). In this way the segmentation favours the construction of regions with smooth edges and a more or less compact form [9]. Although this approach of tackling the fractal nature of landscape yields visually appealing results, it is conceptually unsound. A major pitfall of these three methods is that they start the merging sequence with individual pixels. Apart from being computationally expensive, this approach is inconsistent with the OOA. Pixels can be thought of as square plots on the ground, thus they are artificial units. If an image segment is to coincide with a landcover patch, its boundaries should correspond to some discontinuity on the ground. Therefore single pixels can hardly correspond to landscape objects, since their shape is in no way related with the spatial variation of landcover. A way to tackle this incongruity is to start the region merging process with blobs instead of single pixels. Blobs are tiny homogeneous regions, darker, brighter or of different hue than their surroundings. Just as pixels are the building blocks of an image from a physical point of view, so are blobs the perceptual basic units. Blobs may be contoured via the watershed transform [10], the prime morphological segmentation method. Despite being customarily used in Computer Vision and Medical Radiology, it has been hardly applied to Remote Sensing. This is mainly due to the lack of definite shape (and even crisp boundaries) of the objects of interest, and to the multiband and multiscale nature of the images [11]. However, if the pixel-based paradigm
is finally abandoned by the Remote Sensing community, it can be expected that gradient watersheds will also be used customarily in the analysis of RS imagery. Before describing the SCRM algorithm, it is worth noting that a segmentation sequence consisting of image smoothing and/or gradient magnitude simplification, watershed transform plus region merging, has already been used in different contexts [12,13,14,15]. However, none of these studies was related to landcover mapping. Besides, except for the watershed transform, the algorithms proposed here are new and not based upon the ones used by those authors. Furthermore, our method is conceptually consistent with the OOA, an asset that many segmentation algorithms lack. 3.
ALGORITHM DESCRIPTION
The sequence is the following (Fig.1). The input image (previously ortho-rectified to some cartographic projection) is eventually resampled to a suitable pixel size and then is filtered in order to get rid of superfluous gradient minima created by texture. The output of the filter (Gradient Inverse Weighted Edge Preserving Smoothing, GIWEPS [6]) is an almost piecewise constant image, in which each uniform region is the area of influence of a gradient minimum. The gradient magnitude of the dissimilarity measure is computed, and the output image is searched for local minima. The area of influence of each minimum is contoured and labelled with the watershed algorithm. Then the resulting regions are merged iteratively by increasing dissimilarity until they all exceed the size of the minimum mapping unit (MMU). Finally, the labelled image with the baseline partition is converted into a vector layer. Attributes of output polygons could be optionally compiled at this last stage. 3.0. Image resampling In order to run the SCRM procedure, the user must introduce three parameters: i) the desired mean size of output segments (MSS, in hectares); ii) the minimum size required for segments (MMU, in hectares); and iii) the desired spatial accuracy of boundaries (BSA, in metres). BSA is used to define the working pixel size. If the original pixel size is much smaller than BSA, the image is resampled to half BSA by simple pixel averaging. In that way, BSA is roughly the mean distance between consecutive vertices in the output vector layer. The resampling is done in these cases because ultra high resolution, although always good for identification, is not suitable for drawing boundaries that are intended to depict landcover variations at coarser scales. This in turn is due to the fractal nature of landscape, manifested by the fact that the length of the boundary enclosing any given patch increases indefinitely as resolution increases (Fig. 5).
RS ortho-image (single or multiband) GIWEPS
Filtered image
Gradient
Gradient magnitude image
Watershed
Watershed Partition
SCRM Baseline Partition
Vectorise
Attribute database Figure 1. SCRM workflow
Vector layer
3.1. Image smoothing Due to the hierarchical patchiness of landscape, RS images of any resolution show texture of varying degrees across all their extension. In addition, there may be some noise added by atmospheric effects or the imaging instrument during the acquisition. If the gradient magnitude image is computed without any conditioning of the image, the computation will result in an intricate structure full of edges and local minima, especially in areas with coarse texture. Therefore the structure of the image has to be simplified so that gradient minima produced by texture are removed. The simplification should be performed without altering the resolution of the image, that is, it should act only upon the unresolved elements of the scene that produce texture, leaving untouched the elements corresponding to edges. Such process is commonly called Edge Preserving Smoothing (EPS) [16]. Unlike conventional smoothing techniques like simple averaging or gaussian filtering, EPS filters adapt the process to the structure of the image, so that the local operator is different at each position. In GIWEPS, the new digital number (DN) of a given pixel is the weighted mean of the DNs of its eight neighbours. The weight of each neighbour is proportional to its similarity to that pixel, and the degree of proportionality is governed by a diffusivity parameter. The filter is applied iteratively, up to a point where change between consecutive output images is negligible. Output images beyond this point still resemble the original image during very long time (thousands of iterations). That convergence to a non-flat image enables the analogy with a physical system that reaches a steady state far from equilibrium. With this view, the image is conceived as the initial state of a planar dynamic network consisting of triangular meshes made up of nodes (pixels) connected through links via which the nodes interact during several cycles. This iterative interaction can be seen as non-linear diffusion process that can be formalised by partial differential equations with the original image as initial condition [17]. By applying such process to the image, it evolves to a piecewise constant image. This evolution can be viewed as grouping pixels into various perceptual units (blobs), corresponding to different basins of attraction. Hence the image is allowed to self-organize into structural functional units in which pixels interact more with other pixels within their unit than with pixels of neighbouring units. This behaviour in some way reflects the patchy structure of the underlying landscape. 3.2. Gradient magnitude image Suppose that a given grey-level image is a Digital Elevation Model (DEM), then the gradient magnitude image is the slope map that corresponds to that DEM. In other words, at each pixel of a grey-level image, the
gradient magnitude is the slope of the steepest descent line crossing that pixel. In the case of multiband images, the slope describes the variations in similarity of adjacent pixels across the image. The dissimilarity measure used here is the Euclidean distance between points (pixel signatures) in the feature space. Then gradient minima are those pixels whose value is lower than the one of their eight neighbours in the gradient magnitude image. In the unusual case of plateaus (regions with equally low-valued pixels), there are no proper minima, and the centroid of the plateau is selected as a local minimum representing the region. If gradient minima are assimilated to perceptual attractors, then their basins of attraction are the primal regions building the spatial structure of the image. By adopting such analogy, it is assumed that the area of influence of each gradient minimum is perceived as a blob in the filtered image, i.e. as a homogeneous small region, darker, brighter or of a different hue than its surroundings. 3.3. Watershed partition The application of the topographic concept of watershed to the field of image analysis was introduced in the 70s [18] and implemented into an efficient algorithm in the 90s [10]. The idea is to think of the gradient magnitude image not as a slope map but as a DEM in itself. The goal is to find the drainage divides, or watersheds, of that virtual territory. The watersheds define a network of ridges that enclose the dales, or catchment basins, where each drop of rain would drain. Note that the gradient magnitude image represents a DEM from a peculiar landscape, similar to a lunar plain full of craters with ridges of different heights, where each crater corresponds to a blob in the filtered image. In this sense, this algorithm is basically a blob-contouring tool. Therefore, it is more than just one-among-many segmentation methods: it is a vision tool for applying semiophysics [19] to image analysis. Indeed, the gradient watersheds algorithm provides a first step in the transformation of a numerical representation (a digital image) of a territory into a symbolic objectoriented representation (a thematic vector layer). The watershed transform simulates a gradual immersion. Suppose that the bottoms (gradient minima) of craters are springs where pressurized underground water upwells. Then the water will begin to flood areas adjacent to the spring. Suppose further that the flow at each spring is such that the altitude of the water plane of the submersed areas is the same for all the territory (hence the analogy with immersion rather than flooding). Now, in places where the water coming from two different bottoms would merge, we build a dam of 1-pixel thickness, slightly taller that the highest crater of the territory. When the latter is completely submersed, we stop the immersion. The resulting dams are the watersheds of the territory, which in turn define a
complete partition of the image. In the output image representing the partition, watershed pixels are set to 0, whereas non-zero pixels have as DN the numeric label of the segment to which they belong. 3.4. Region merging In this step the regions of the watershed partition (blobs) are aggregated into segments exceeding the MMU size. The most distinctive feature of SCRM is that it imposes no threshold on the similarity of the regions to be merged. Many region merging algorithms include a size constraint [20,5,21], but of all them set thresholds on the dissimilarity measure. In SCRM, the merging proceeds until all regions in the partition are larger than the specified size, and the merging sequence is such that the homogeneity of the resulting regions is maximal given the size constraint. The dissimilarity criterion used to merge segments is the Euclidean distance between signatures in a feature space where each dimension corresponds to a band of the image. The signature of a segment is simply the mean value in each band of pixels belonging to it. The signature of a new segment is the weighted –by sizemean of the signatures of the two merged segments. In this way, segment signatures are computed from the original image only once, at the beginning of the merging procedure. The same can be said about the adjacency table (an array returning the list of neighbours of any given segment), which is first computed from the watershed partition and then updated using Boolean algebra. From the adjacency table (AT) and the signature list (SL), the identification of the most similar neighbour (MSN) to each segment is trivial. The table-based updating of both signatures and adjacency enables the use of the global mutual best fitting strategy, which otherwise would be too slow. That is to say that in each iteration only a candidate pair is merged, the one for which the dissimilarity criterion is minimal. Then the AT, SL and MSN arrays are updated, and new iteration proceeds. The process continues this way until the sum of i) the number of segments currently larger than MMU, plus ii) the result of dividing by MSS the area currently occupied by segments smaller than MMU, is less than the result of dividing the area of the image by MSS. This is a partial stop criterion that guarantees that the final mean size of segments will be close to the desired one. Reached this point, the size of segments is taken into account in the merging procedure, so that the best fitting pair is allowed to merge only if at least one of both segments is smaller than MMU. In this way homogeneous regions are formed first, and then dissimilar gaps smaller than MMU are progressively incorporated to the former until all segments are larger than MMU.
The actual merging of two segments consists in replacing the label of one of them with the label of the other in the final label list (FLL). FLL is an array of length equal to the number of segments –blobs- in the watershed partition. At any point during the merging process, there is a link that keeps track of blobs compounding each segment, so that FLL can be updated easily. Once the merging is completed, a new raster is created from the watershed partition by replacing the DN of pixels inside each blob with the new label registered in the corresponding position of FLL. Finally, watershed (0-valued) pixels lying in the interior of final segments are filled with the numeric label of the corresponding segment. 3.5. Vectorization Once the baseline partition is obtained, an optional last step is to convert it into a vector layer. In order to proceed, the centres of boundary (0-valued) pixels are considered the initial vertices forming the arcs. Note that this is analogous to consider boundary pixels as a transition zone between patches that can be represented by its medial axis. The nodes (junctions between arcs) are identified, so that each polygon is defined by the set of arcs bounding the corresponding segment. In order to give a smooth appearance to arcs (Fig. 3), a spline interpolation is applied to the centroids of each three consecutive vertices. Once the partition is vectorized, an associate database is filled with radiometric information about each segment. The resulting vector layer may be used not only for automated classification, but as a guiding template for photointerpretation. In this event, the interpreter needs not to digitise arcs, she just has to select and erase (through e.g. mouse clicks) the arcs she considers not relevant. 4.
EXAMPLES
The SCRM algorithm has been implemented in IDL (www.rsinc.com) and tested in several images. Preliminary results seem to adapt reasonably well to the spatial structure of the image. As an example, Fig. 2 shows a 5 x 5 km2 Landsat ETM+ (path 200 row 32) subscene, acquired on 22 Aug 2000 over a rural area in the Guadalajara province, Spain. The segmentation was produced using bands 4, 5 and 3, and selecting MSS=25 ha, MMU= 5 ha, and BSA=25 m. The central segment of the image is a burn scar (Fig. 3) in the border between a pine forest and a juniper sparse woodland (underneath). SCRM may also be used in multitemporal analysis. As an example, Fig. 4 shows the results of applying SCRM to a NDVI multitemporal 5x5 km2 image derived from three Landsat ETM+ images acquired respectively on 20 May, 28 June and 16 July 2000 over Barrax, Spain.
The input parameters were MSS=25 ha, MMU= 2 ha, and BSA=50 m.
5. DISCUSSION
Finally, Fig. 5 is a 0.4x0.4 km2 detail of panchromatic orthophoto showing a burn scar. SCRM was applied to the original image (1 m pixel) and to a coarser version (10 m pixel). The boundary derived at the fine resolution is far more intricate than the one obtained at 10 m resolution.
After having applied SCRM to many images, none of the output partitions produce a visual impression of a ‘bad segmented’ image. For most segments, there seems to be some sense of cohesiveness throughout the area enclosed within the segment, and contrariwise, some sense of discontinuity across the boundary between the segment and its neighbours.
Fig. 2. SCRM result in a multispectral image
Fig. 3. Detail of the vectorisation
Fig. 4. SCRM result in a multitemporal NDVI image
Fig. 5. Two delineations of a burn scar at different resolutions
The output partition is a model of the territory that is constructed by two separate mechanisms of generalization: the regularisation produced by the sensor (and later by the filter) and the aggregation of primal regions (the areas of influence of gradient minima) according to their radiometric similarity. The segmentation method used to implement the second mechanism should ideally be uncommitted, i.e. it should need no a priori knowledge from the user, so that the only input required are the size constraints, which together with the spatial accuracy of boundaries define the level of generalisation of the uncommitted model. However, different models may be derived from the same input data and size constraints using different resampling, filtering and merging rules. Hence, it is not clear what combination of both regularisation and aggregation is the best For example, one alternative would be to perform the segmentation at two resolutions. The coarser resolution would be the coarsest one that can be used to detect reliably patches close to the minimum admissible size. The finer resolution would be half the spatial accuracy required for the final product. Then the final boundary enclosing each segment of the coarser partition could be obtained as the outer boundary of the conglomerate of overlapping segments from the finer partition. Since fine segments may overlap with more than one coarse segment, a decision has to be made on what is the coarse segment to which each fine segment belongs. This decision is not as straightforward as one might think, since there are many ambiguities that cannot be solved, as we actually experienced when we tentatively tried this alternative. Ambiguities and inconsistencies also appear in low contrasted areas. While the shape of high contrasted regions does not suffer significant changes by varying the SCRM internal parameters (filter diffusivity, dissimilarity measure, intermediate stop criterion), areas lacking strong edges are combined in very different ways, producing disparate regions. A similar situation would occur also for human interpreters, whose individual interpretations of low contrasted areas are likely to differ too. Although this problem is common to any segmentation method [9], a sensitivity analysis would help us to understand better this issue. In the end, such inconsistencies may actually arise because the representations of reality are manifold, and often, none of them can be said to be strictly preferred to the others. Perhaps for this reason, visual check remains the basic evaluation procedure for newly developed algorithms, although there are some empirical methods [22] that try to mitigate the inevitable subjectiveness of the evaluation. Besides, error reduction may be only one of several conflicting goals in landcover mapping, and error itself is susceptible of different definitions. In short, there is no single correct
patch hierarchy fitting a given landscape, since hierarchies and the maps that represent them are human constructs [23]. Each individual and institution have different interests, conceptions and methods, therefore they may hold different views of the same reality. Since users and operations are manifold, the issue of producing the best model requires a deeper analysis under the framework provided by multiobjective decision-making theory [24]. Such analysis is beyond the scope of this work, although it should be addressed in future research in order for OOA to constitute an operational standard in image analysis for landcover mapping. 6.
CONCLUSIONS
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