This problem is addressed in Estimating Complexity of 2D Shapes (2005). The notion of "complexity" seems to agree at least qualitatively with what the OP calls "uniformity". The complexity measure $C$ of a 2D shape is quantified by the combination of three criteria – (a) entropy of the global distance distribution, (b) entropy of local angle distribution, (c) shape randomness. The figure below shows results for 6 shapes, digitizeddiscretized by a set of points. Small $C$ means low complexity.
This problem is addressed in Estimating Complexity of 2D Shapes (2005). The notion of "complexity" seems to agree at least qualitatively with what the OP calls "uniformity". The complexity measure $C$ of a 2D shape is quantified by the combination of three criteria – (a) entropy of the global distance distribution, (b) entropy of local angle distribution, (c) shape randomness. The figure below shows results for 6 shapes, digitized by a set of points. Small $C$ means low complexity.
This problem is addressed in Estimating Complexity of 2D Shapes (2005). The notion of "complexity" seems to agree at least qualitatively with what the OP calls "uniformity". The complexity measure $C$ of a 2D shape is quantified by the combination of three criteria – (a) entropy of the global distance distribution, (b) entropy of local angle distribution, (c) shape randomness. The figure below shows results for 6 shapes, discretized by a set of points. Small $C$ means low complexity.
This problem is addressed in Estimating Complexity of 2D Shapes (2005). The notion of "complexity" seems to agree at least qualitatively with what the OP calls "uniformity". The complexity measure $C$ of a 2D shape is quantified by the combination of three criteria – (a) entropy of the global distance distribution, (b) entropy of local angle distribution, (c) shape randomness. The figure below shows results for 6 shapes, digitized by a set of points. Small $C$ means low complexity.
