In[13]:=
f[x_, y_] := x - y^2 Cos[y] g[x_, y_] := -y + x Sin[x] contourData = Map[First, Cases[Graphics[ ContourPlot[f[x, y], {x, -10, 10}, {y, -10, 10}, Contours -> {0}, PlotPoints -> 50]], _Line, Infinity]]; signs = Sign[Apply[g, contourData[[5]], 2]] // Short
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Out[13]=
{-1, -1, -1, -1, 1, 1, 1, 1, 1, <<57>>, 1, 1, 1, -1}
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1. Harvesting the Seeds