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The main contribution of this paper is a new column-by-column method for thedecomposition of generating functions of convex polyominoes suitable forenumeration with respect to various statistics including but not limited tointerior vertices, boundary vertices of certain degrees, and outer siteperimeter. Using this decomposition, among other things, we show that  A) the average number of interior vertices over all convex polyominoes ofperimeter $2n$ is asymptotic to $\frac{n^2}{12}+\frac{n\sqrt{n}}{3\sqrt{\pi}}-\frac{(21\pi-16)n}{12\pi}.$  B) the average number of boundary vertices with degree two over all convexpolyominoes of perimeter $2n$ is asymptotic to$\frac{n+6}{2}+\frac{1}{\sqrt{\pi n}}+\frac{(16-7\pi)}{4\pi n}.$ Additionally,we obtain an explicit generating function counting the number of convexpolyominoes with $n$ boundary vertices of degrees at most three and show thatthis number is asymptotic to $\frac{n+1}{40}\left(\frac{3+\sqrt{5}}{2}\right)^{n-3}+\frac{\sqrt[4]{5}(2-\sqrt{5})}{80\sqrt{\pin}}\left(\frac{3+\sqrt{5}}{2}\right)^{n-2}. $ Moreover, we show that theexpected number of the boundary vertices of degree four over all convexpolyominoes with $n$ vertices of degrees at most three is asymptotically $\frac{n}{\sqrt{5}}-\frac{\sqrt[4]{125}(\sqrt{5}-1)\sqrt{n}}{10\sqrt{\pi}}. $  C) the number of convex polyominoes with the outer-site perimeter $n$ isasymptotic to $\frac{3(\sqrt{5}-1)}{20\sqrt{\pi  n}\sqrt[4]{5}}\left(\frac{3+\sqrt{5}}{2}\right)^n,$ and show the expectednumber of the outer-site perimeter over all convex polyominoes with perimeter$2n$ is asymptotic to$\frac{25n}{16}+\frac{\sqrt{n}}{4\sqrt{\pi}}+\frac{1}{8}.$ Lastly, we provethat the expected perimeter over all convex polyominoes with the outer-siteperimeter $n$ is asymptotic to $\sqrt[4]{5}n$.

Convex polyominoes revisited: Enumeration of outer site perimeter, interior vertices, and boundary vertices of certain degrees