polynomial curve fitting on image

Hello all, below is one of the images i am working on

I would like to perform third degree polynomial curve fitting on the green and red boundary segments and find their intersection points.Further using that intersection point i would like to segment the image into right and left parts. But I am not getting the right fitting, what am i doing wrong, can anyone please help? I have attactched the code and the original image. Any help is deeply appreciated, thank you in advance.

clc;
clear;
close all;
a=rgb2gray(imread('FLIR0179.jpg'));
a=a(500:800,50:1080);
en= imsharpen(a,'Radius',4,'Amount',2);
ed=edge(en,'canny',0.2,0.5);
bw1=bwareaopen(ed,20);
se = strel('disk',4);
bw=imdilate(bw1,se);
col1 = 422;
row1 = min(find(bw(:,col1)));
boundary1 = bwtraceboundary(bw,[row1, col1],'N');
col2 = 629;
row2 = min(find(bw(:,col2)));
boundary2 = bwtraceboundary(bw,[row2, col2],'N');
figure;
imshow(bw);
hold on;
plot(boundary1(:,2),boundary1(:,1),'g','LineWidth',3);
plot(boundary2(:,2),boundary2(:,1),'r','LineWidth',3);
hold off
x1 = boundary1(:, 2);y1 = boundary1(:, 1);
x2 = boundary1(:, 2);y2 = boundary1(:, 1);
P1=polyfit(y1,x1,3);
P2=polyfit(y2,x2,3);
yy = linspace( 1, size(bw,1));
p1=polyval( P1, yy);
p2=polyval( P2, yy);
figure; 
imshow(a, 'border', 'tight' );
hold on
plot(p1,yy);
plot(p2,yy);
hold off