Fuzzy squareness: A new approach for measuring a shape.

• A new fuzzy squareness measure for evaluating how much a given shape is a fuzzy square is introduced. • Such a measure ranges through (0, 1], and reaches maximal value 1 iff for a fuzzy square. • The new fuzzy squareness measure is invariant w.r.t. similarity transformations. • The new measure is naturally defined and theoretically well-founded. • Effectiveness of the new measure is illustrated through classification tasks performed on three large well-known image datasets. In this paper, we define a new fuzzy squareness measure to quantify how much a given fuzzy shape matches a fuzzy square. The new fuzzy shape-based measure is naturally defined and theoretically well-founded, resulted in that its behavior can be understood and predicted in advance. It runs through the interval (0 , 1 and takes the maximum value equals 1 if and only if the shape measured is a fuzzy square. The new fuzzy squareness measure is also invariant to similarity transformations. Several various experiments to illustrate the behavior of the new measure, and to verify all the theoretically proven results are also shown. Effectiveness and usefulness of the new fuzzy squareness measure are demonstrated in the tasks of object classification performed on three large well-known modern image datasets such as MPEG-7 CE-1, Swedish Leaf, and Portuguese Leaves datasets. [ABSTRACT FROM AUTHOR]