# A Multi-World Approach to Question Answering about Real-World Scenes based on Uncertain Input

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4 auxiliary relations spatial Predicate Definition closeabove(a, B) above(a, B) and (Y min(b) < Y max(a) + ɛ) closeleftof(a, B) leftof(a, B) and (X min(b) < X max(a) + ɛ) closeinf rontof(a, B) inf rontof(a, B) and (Z min(b) < Z max(a) + ɛ) X aux(a, B) X mean(a) < X max(b) and X min(b) < X mean(a) Z aux(a, B) Z mean(a) < Z max(b) and Z min(b) < Z mean(a) h aux(a, B) closeabove(a, B) or closebelow(a, B) v aux(a, B) closeleftof(a, B) or closerightof(a, B) d aux(a, B) closeinf rontof(a, B) or closebehind(a, B) leftof(a, B) X mean(a) < X mean(b)) above(a, B) Y mean(a) < Y mean(b) inf rontof(a, B) Z mean(a) < Z mean(b)) on(a, B) closeabove(a, B) and Z aux(a, B) and X aux(a, B) close(a, B) h aux(a, B) or v aux(a, B) or d aux(a, B) Table 1: Predicates defining spatial relations between A and B. Auxiliary relations define actual spatial relations. The Y axis points downwards, functions X max, X min,... take appropriate values from the tuple predicate, and ɛ is a small amount. Symmetrical relations such as rightof, below, behind, etc. can readily be defined in terms of other relations (i.e. below(a, B) = above(b, A)). color [16] (Figure 1 - middle part). Every object hypothesis is therefore represented as an n-tuple: predicate(instance id, image id, color, spatial loc) where predicate {bag, bed, books,...}, instance id is the object s id, image id is id of the image containing the object, color is estimated color of the object [16], and spatial loc is the object s position in the image. Latter is represented as (X min, X max, X mean, Y min, Y max, Y mean, Z min, Z max, Z mean ) and defines minimal, maximal, and mean location of the object along X, Y, Z axes. To obtain the coordinates we fit axis parallel cuboids to the cropped 3d objects based on the semantic segmentation. Note that the X, Y, Z coordinate system is aligned with direction of gravity [15]. As shown in Figure 2b, this is a more meaningful representation of the object s coordinates over simple image coordinates. The complete schema will be documented together with the code release. We realize that the skilled use of spatial relations is a complex task and grounding spatial relations is a research thread on its own (e.g. [17], [18] and [19]). For our purposes, we focus on predefined relations shown in Table 1, while the association of them as well as the object classes are still dealt within the question answering architecture. Multi-worlds approach for combining uncertain visual perception and symbolic reasoning Up to now we have considered the output of the semantic segmentation as hard facts, and hence ignored uncertainty in the class labeling. Every such labeling of the segments corresponds to different interpretation of the scene - different perceived world. Drawing on ideas from probabilistic databases [14], we propose a multi-world approach (Figure 1 - lower part) that marginalizes over multiple possible worlds W - multiple interpretations of a visual scene - derived from the segmentation S. Therefore the posterior over the answer A given question Q and semantic segmentation S of the image marginalizes over the latent worlds W and logical forms T : P (A Q, S) = P (A W, T )P (W S) P (T Q) (2) W T The semantic segmentation of the image is a set of segments s i with the associated probabilities p ij over the C object categories c j. More precisely S = {(s 1, L 1 ), (s 2, L 2 ),..., (s k, L k )} where L i = {(c j, p ij )} C j=1, P (s i = c j ) = p ij, and k is the number of segments of given image. Let Ŝ f = { (s 1, c f(1) ), (s 2, c f(2) ),..., (s k, c f(k) )) } be an assignment of the categories into segments of the image according to the binding function f F = {1,..., C} {1,...,k}. With such notation, for a fixed binding function f, a world W is a set of tuples consistent with Ŝf, and define P (W S) = i p (i,f(i)). Hence we have as many possible worlds as binding functions, that is C k. Eq. 2 becomes quickly intractable for k and C seen in practice, wherefore we use a sampling strategy that draws a finite sample W = (W 1, W 2,..., W N ) from P ( S) under an assumption that for each segment s i every object s category c j is drawn independently according to p ij. A few sampled perceived worlds are shown in Figure 2a. Regarding the computational efficiency, computing T P (A W i, T )P (T Q) can be done independently for every W i, and therefore in parallel without any need for synchronization. Since for small N the computational costs of summing up computed probabilities is marginal, the overall cost is about the same as single inference modulo parallelism. The presented multi-world approach to question answering on real-world scenes is still an end-to-end architecture that is trained solely on the question-answer pairs. 4

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