# Question about the pose from homography and fundamenta matrix

I have get projection matrix from homography and camera parameter for AR. For checking if the result is good, I tested if ROI (0, 0) (w, 0), (w, h), (0,h) in the coordinate of reference image can be visualized in different image at different view. I assumed that ROI 4 points have zero depth. The result is successful.

Thesedays, I implemented the same function from fundamental matrix. 1. get Fundamental Matrix 2. Essential matrix from Fundamental 3. decompose essential mat into rotation & translation matrix 4. get projection matrix from camera parameter & rotation & translation Matrix.

Like the case I used projection mat from homography, I transformed 4 ROI in reference into the other image at different view. But the result is different from one by homography. Non feasible result was shown as the strange ROI box.

I was wonderingn if the projection matrix by homography is different from one by fundamental matrix?

please let me know how to transform ROI in reference image into the same scenen at different view.