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Scenes are composed of numerous objects, textures and colors which are arranged in a variety of spatial layouts. This presents the question of how visual complexity is represented by a cognitive system. In this paper, we aim to study the representation of visual complexity for real-world scene images. Is visual complexity a perceptual property simple enough so that it can be compressed along a unique perceptual dimension? Or is visual complexity better represented by a multi-dimensional space? Thirty-four participants performed a hierarchical grouping task in which they divided scenes into successive groups of decreasing complexity, describing the criteria they used at each stage. Half of the participants were told that complexity was related to the structure of the image whereas the instructions in the other half were unspecified. Results are consistent with a multi-dimensional representation of visual complexity (quantity of objects, clutter, openness, symmetry, organization, variety of colors) with task constraints modulating the shape of the complexity space (eg the weight of a specific dimension).