Which way to solve this

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In the first you have to increase resolution of image in the next stage for detect rectangle you need use edge of image because the edge detection insensitive to changes of illumination in the image you have to use a method robust to illumination in the next stage you have to use hough line for detection line & rectangle this link help you to detection rectangle.

You have 2 peaces of information:
1) shape
If you want to detect a shape all at once with the principle of Hough transform without relying on multiple lines you can perform a Generalized Hough Transform search.
On this website there is a base for your own implementation of GHT as well as a nice tutorial. Or you can also try a chamfer matching. But I don’t like the code provided with OpenCv.
The code in the link I provided is not so beautiful but it’s effective and easy to understand, the one with OpenCv just the reverse. Try and see if there is a different implementation of it. Both methods tolerate a small amount of rotation and warping.

2) colour
You have to implement a Bayesian method which provides the probability of every pixel (or better group of pixels to smooth noise) to be inside the white rectangle: P(rectangle|colour).

At the end you should find a way to put together information 1 and 2