With the large dataset, I can perform inter-species and inter-population comparative analysis of wings pattern statistics in each common inter-vein regions, and compute an average wing.

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To enable the inter-species and inter-population comparative analysis, a critical step is to map all wings to a common reference wing space. The task is not trivial and requires the wing boundaries and the common primary veins to match. Existing methods cannot accomplish the goal. In a failed try, I used a software based on quasi-conformal mapping [4]. However, due to angle changes during the nonlinear mapping, the result is not physically reasonable with curly veins (Figure below, (d)). Instead, I am implementing a custom-designed mapping technique. First, I put corresponding points in each wing, selected in systematic ways (end points of veins, and evenly spaced points on the veins in between the end points). I then define triangles in a systematic way using the corresponding points for all wings. Then, through affine transformation for each pair of triangles, I can find a map that match the shape, veins and preserve the straightness of the veins (Figure below, (c)). Via further refinement of the points and triangles, I can obtain a finer map with better boundary matching. I am also investigating polynomial least-square mapping using the points only (without the triangles), for a differentiable and better map.