Need Help Regarding Logmap

Hi,

I'm trying to implement Logmap (Log-Polar Mapping)of Images..Here i don't want to use Matlab functions (built-in) have to do this simply using loops .As i have to move the algo to FPGA next.

I have Implemented using very less (almost no Matlab function except pol2cart), But the results are not smooth enough , can any one explain me hoe to improve or solve the checker board type problem even after using averaging in neighbours

Im putting the code here its a lil dirty still, also comments are removed

        clc
    clear
    close all

    a  = imread('cameraman.tif');

    [r c]=size(a);

    ps=1; % Padding size

    aa=zeros(r+10,c+10);

    aa(ps+1:r+ps,ps+1:c+ps)=a;
    % Claculating the center
    xc = 0.5 + size(a,2)/2;
    yc = 0.5 + size(a,1)/2;

    % Number of Rings
    nr = min(size(a,2),size(a,1));

    rmin = 0.1; %Innermosr ring radai
    rmax = min(xc,yc); %OuterMost ring radai

    nw = (-2*pi*(nr-1)) / log(rmin/rmax); % Number of wedges with out center

    rmin = 0.1;
    rmax = min([xc-0.5,yc-0.5]);
    deltaTheta = (2*pi) / nw;

    step_r=(log(rmax)-log(rmin))/(nr-1); % Step for equal spaced items
    step_t=((2*pi)-deltaTheta)/(nw-1);

    lp_img=[];
    lp_img_2=[];
    x_d=[];
    y_d=[];

    x=1;
    y=1;
    pix=[];
    for logRho=log(rmin):step_r:log(rmax)
        rho = exp(logRho);
            for theta=0:step_t:((2*pi)-deltaTheta)

                [Y,X] = pol2cart(theta,rho);

                X = (X+xc+ps);
                Y = (Y+yc+ps);

                X=round(X);
                Y=round(Y);

         % x_d(x,y)=X;
         % y_d(x,y)=Y;

            pix=aa(abs(X-ps):X+ps,(abs(Y-ps):Y+ps));
            [rr cc]=size(pix);

         av=sum(sum(pix))/(rr*cc);

          lp_img(y,x)= av;
            y=y+1;

        end
      y=1;  
      x=x+1;
    end

    figure, imagesc(lp_img); colormap gray