# Monthly Archives: June 2008

## Random Image Segmentation

I’ve been playing around today with an image decomposition method. Given some observed image , one seeks an image so as to minimize Where the first sum is over all pixels , and the second sum is over all neighboring … Continue reading

## Markov’s Inequality

While looking at Tao’s post on the law of large numbers, I claimed to Alap that Markov’s inequality was “obvious”. Asked to back that up, though, I couldn’t remember why it was obvious. Take some distribution . For simplicity, assume … Continue reading

## More Implicit Functions

(This time, including derivatives.) Closed form solutions are possible for some of these, I know. …which of course has a constant derivative. Matlab code: function implicit_funcs options = optimset(‘TolX’,1e-15,’MaxFunEvals’,1e5,’MaxIter’,1e5); fsize = 16; e = 1e-5; f1 = @(x) 5*x; f2 … Continue reading

## Implicit Functions

Matlab code: function implicit_funcs fsize = 16; f1 = @(x) x; f2 = @(x) 1.5*x; xAR = -2.5:.05:2.5; for n=1:length(xAR) x = xAR(n); myfun = @(y) abs(y-f1(x)) + (y-f2(x))^2; y_star(n) = fminsearch(myfun,0); end plot(xAR,f1(xAR),’k-‘,xAR,f2(xAR),’k–‘,xAR,y_star,’r.’,’LineWidth’,2) legend(‘f1′,’f2′,’y*’) title(‘y*(x) = arg min_y = … Continue reading