By using multiple cues, such as disparity, motion parallax, perspective, our brains can construct 3D representations of the world from the 2D projections on our retinas. We live in a three-dimensional (3D) spatial world however, our retinas receive a pair of 2D projections of the 3D environment. 3Department of Psychological and Brain Sciences, Computational Neuroscience and Vision Lab, Center for Systems Neuroscience, Boston University, Boston, MA, United States.2Laboratory for Human Cognition and Learning, RIKEN Center for Brain Science, Wako, Japan. 1Laboratory of Perceptual and Cognitive Dynamics, Electrical & Computer Engineering, Ritchie School of Engineering & Computer Science, University of Denver, Denver, CO, United States.We follow this by examining a geodesic bicombing on the nonempty compact subsets of X" role="presentation" style="box-sizing: inherit display: inline line-height: normal word-spacing: normal overflow-wrap: normal white-space: nowrap float: none direction: ltr max-width: none max-height: none min-width: 0px min-height: 0px border: 0px padding: 0px margin: 0px position: relative ">XX, assuming X" role="presentation" style="box-sizing: inherit display: inline line-height: normal word-spacing: normal overflow-wrap: normal white-space: nowrap float: none direction: ltr max-width: none max-height: none min-width: 0px min-height: 0px border: 0px padding: 0px margin: 0px position: relative ">XX is a proper metric space.Haluk Ogmen 1, Kazuhisa Shibata 2 and Arash Yazdanbakhsh 3* If X" role="presentation" style="box-sizing: inherit display: inline line-height: normal word-spacing: normal overflow-wrap: normal white-space: nowrap float: none direction: ltr max-width: none max-height: none min-width: 0px min-height: 0px border: 0px padding: 0px margin: 0px position: relative ">XX is a normed space or an R" role="presentation" style="box-sizing: inherit display: inline line-height: normal word-spacing: normal overflow-wrap: normal white-space: nowrap float: none direction: ltr max-width: none max-height: none min-width: 0px min-height: 0px border: 0px padding: 0px margin: 0px position: relative ">RR-tree, this same method produces a consistent convex bicombing on CB(X)" role="presentation" style="box-sizing: inherit display: inline line-height: normal word-spacing: normal overflow-wrap: normal white-space: nowrap float: none direction: ltr max-width: none max-height: none min-width: 0px min-height: 0px border: 0px padding: 0px margin: 0px position: relative ">CB(X)CB(X). We show that if (X,d)" role="presentation" style="box-sizing: inherit display: inline line-height: normal word-spacing: normal overflow-wrap: normal white-space: nowrap float: none direction: ltr max-width: none max-height: none min-width: 0px min-height: 0px border: 0px padding: 0px margin: 0px position: relative ">(X,d)(X,d) is a metric space which admits a consistent convex geodesic bicombing, then we can construct a conical bicombing on CB(X)" role="presentation" style="box-sizing: inherit display: inline line-height: normal word-spacing: normal overflow-wrap: normal white-space: nowrap float: none direction: ltr max-width: none max-height: none min-width: 0px min-height: 0px border: 0px padding: 0px margin: 0px position: relative ">CB(X)CB(X), the hyperspace of nonempty, closed, bounded, and convex subsets of X" role="presentation" style="box-sizing: inherit display: inline line-height: normal word-spacing: normal overflow-wrap: normal white-space: nowrap float: none direction: ltr max-width: none max-height: none min-width: 0px min-height: 0px border: 0px padding: 0px margin: 0px position: relative ">XX (with the Hausdorff metric).
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