use SIFt detector with SURF algorithm for image matching

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First of all, SURF is not better than SIFT, most papers and evaluations will confirm this. Second, the incompatibily comes with the fact that both algorithms use different strategies for computing orientations and scale of the interest points aka keypoints. You can try to find methods to "convert" these attributes but using them on the fly will not give you good results as you have already seen.

By the way, SURF incrases the size of the box filters to accomplish the scale space approach of SIFT using gaussian convolution. The intergral images are mainly used for performance reasons.

Surf is better then sift , but it depends on the images you are using , if you query images are nearly same or less in amount then your going right , but if they are different and large in amount then you need to change the algorithms , But your question about keypoints using SIFT and descriptor of SURF is not giving good result is true , how you can take keypoints from one image using one algorithm and find descriptor from the same image using same keypoints with other algorithm , to me this is invalid , BUT its not 100% right because there is always a room in programming where you can deal with many impossibilities through logics :)

EDIT :

SIFT computes an image pyramid by convolving the image several times with large Gaussian kernels, while SURF accomplishes an approximation of that using integral images.