# A Multilevel Road Alignment Model for Spatial-Query-by-Sketch
## 2 Related Work  
Shape-based query-by-sketch techniques have been widely used for image retrieval. [PERSON] [26] asserted that the shape of a sketched object is useful to identify other images containing similarly shaped objects by considering their spatial structures. For that, [PERSON] [27; 28; 29] proposed a global feature scheme based on a qualitative representation in which tripartite line tracks were used to describe polygons and bipartite arrangements were used to describe the relation between two disconnected objects. [PERSON] et al. [30] applied the discrete curve evolution (DCE, [31]) to decompose complete contours and created the MPEG-7 (Moving Picture Experts Group) database of contour segments. Their representation of object parts was invariant to scaling, rotation, and translation; moreover, smaller misalignments in the contours have a robust shape context that allows shape matching. [PERSON] et al. [32] presented a Qualitative Shape Descriptor (QSD) to describe the contour of an object shape extracted from any digital image and also a computational approach to compare the QSDs obtained in order to identify shape correspondences. [PERSON] et al. [33] built the multimodal MindFinder system, which can retrieve sketches from millions of images. Their system allowed users to outline the main shapes by tagging and colouring. [PERSON] et al. [34] improved the MindFinder framework using a shape word descriptors for sketch-based image retrieval and they employed the classical Chamfer Matching Algorithm by [35] to address the shape word matching problems. Furthermore, [PERSON] et al. [34] proposed the use of an inverted index structure to extend the shape word expression to a wide range of image databases. In addition, shape-based road alignment has been applied for vector road network matching. [PERSON] [36] adopted a turning function as the descriptor of the road shapes. [PERSON] et al. [37] proposed a framework based on the least squares adjustment [38; 39] and position constraints to match object geographic shapes. [PERSON] et al. [40] formulated a logistic regression matching method named OILRM (Optimization and Iterative Logistic Regression Matching), which is used to determine the distance between two lines based on their vertices for road matching. [PERSON] et al. [41] compared the angles and directions of linear features and obtained high accuracy results by further comparingthe topological relationships between the matched features. To carry out shape comparison in images, [PERSON] et al. [42] studied three functions (turning, signature, and tangent functions) and three shape descriptors (shape context, LORD, and shape signature). In addition, [PERSON] et al. [42] demonstrated that the turning function can be used to efficiently distinguish objects in terms of their shapes. In particular, the existing studies on shape-based query-by-sketch for image retrieval [26; 27; 28; 29; 30; 31; 33; 34] focused on a small number of objects for comparison, whereas a sketch map may contain typically 12-17 objects [13]. Furthermore, the spatial relationships among objects also must be aligned to carry out Spatial-Query-by-Sketch. In the approach presented in this paper, the main roads from sketch maps are extracted, because they have been demonstrated to exhibit considerable similarities between sketch maps and metric maps [24]. In addition, the characteristics of the main roads are further analyzed and compared quantitatively and qualitatively at three levels: individual road, composite road, and road scene. Consequently, the approach presented here is different from those reported by [PERSON] [36] and [PERSON] et al. [40], in which only quantitative characteristics (e.g., turning functions or distances between vortices) were adopted for road matching. The proposed approach differs from the work by [PERSON] et al. [41] as we surveyed more than one spatial relationship (topological relationship).