Fill gaps for a broken line and get a continious line

Hello,

I have a Sobel output image which is a line. This line is a broken line . I want to interpolate the line where ever white pixels are not detected in that corresponding row and get a continious line.As i need to have a subpixel accuracy i am not able to use Dilate/Erode functions. Please let me know if there are any other functions which can be used to interpolate this line and get me a continious edge.

I am sending here the picture which i need to interpolate and get a continious line.

Looking forward to hear from you.

Thanks Pankaja

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