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Cross-dimensional analysis for improved scene understanding

Visual data have taken up an increasingly large role in our society. Most people have instant access to a high quality camera in their pockets, and we are taking more pictures than ever before. Meanwhile, through the advent of better software and hardware, the prevalence of 3D data is also rapidly expanding, and demand for data and analysis methods is burgeoning in a wide range of industries. The amount of information about the world implicitly contained in this stream of data is staggering. However, as these images and models are created in uncontrolled circumstances, the extraction of any structured information from the unstructured pixels and vertices is highly non-trivial. To aid this process, we note that the 2D and 3D data modalities are similar in content, but intrinsically different in form. Exploiting their complementary nature, we can investigate certain problems in a cross-dimensional fashion - for example, where 2D lacks expressiveness, 3D can supplement it; where 3D lacks quality, 2D can provide it. In this thesis, we explore three analysis tasks with this insight as our point of departure. First, we show that by considering the tasks of 2D and 3D retrieval jointly we can improve performance of 3D retrieval while simultaneously enabling interesting new ways of exploring 2D retrieval results. Second, we discuss a compact representation of indoor scenes called a "scene map", which represents the objects in a scene using a top-down map of object locations. We propose a method for automatically extracting such scene maps from single 2D images using a database of 3D models for training. Finally, we seek to convert single 2D images to full 3D scenes using a database of 3D models as input. Occlusion is handled by modelling object context explicitly, allowing us to identify and pose objects that would otherwise be too occluded to make inferences about. For all three tasks, we show the utility of our cross-dimensional insight by evaluating each method extensively and showing favourable performance over baseline methods.