img=ImageResize[,250];
col=BSplineFunction[ImageData[img]];
f=BSplineFunction[Table[{i+.5(-1)^j,j+.5(-1)^i},{i,7},{j,7}]];
opts={PlotPoints->100,MaxRecursion->0,Mesh->None,ColorFunction->(col[1-#4,#3]&),Axes->None,FrameTicks->None};
Grid[{{ParametricPlot[{u,v},{u,0,1},{v,0,1},Evaluate[opts]],ParametricPlot[{Cos[t]Cos[s],Sin[s]},{t,0,Pi},{s,-Pi/2,Pi/2},Evaluate[opts]]},{ParametricPlot[Evaluate[{u Cos[d]-v Sin[d],v Cos[d]+u Sin[d]}/.d->Pi/2 Norm[{u,v}]],{u,-1,1},{v,-1,1},Evaluate[opts]],ParametricPlot[f[u,v],{u,0,1},{v,0,1},Evaluate[opts]]}}]