Blending three images into a panorama image.
Homography matrixs were calculated between left-middle, middle-right images. Feature points found by SIFT were used to calculate matrix. The process of calculating matrix was implemented from scatch. In order to find robust matrix, RANSAC was used. After finding Homography matrix, backward mapping was used to prevent holes, frequently found in forward mapping.

Using SIFT for keypoint detection & descriptors. This was implemented in SIFT_detect function.
After detecting keypoints, need to find correspondences between keypoints in source and reference image.
The following is the details of function compute_raw_matches, which computes coarse correspondences between keypoints.

1. Find correspondences with descriptors, Euclidean distance was used for matching descriptors.
   
2. Set keypoint's descriptor in source image, then calcuate Euclidean distance with all keypoint's descriptors in reference image.
   
3. Sorting them in ascending order. The lower of the distance between descriptors, the similar with descriptors.
4. Save best & second matching results in raw_matches.

Raw_matches were then filtered, to find good correspondences. This was implemented in filter matches.
First, set the disance ratio (usually between 0.6~0.9). Then, find the ratio between first & second nearest match and compare with distance ratio. If the ratio is smaller than distance ratio, it is estimated as good match. Iterate this process over the raw_matches, and save the good matche into good_matches.

We can compute homograhpy matrix based on good matches. The pictures below show how to calculate matrix.
It is over-determined problem, which only needs 4 correspondencess. However, there are more than 4 correspondences in good_matches, we can use RANSAC in the presence of outliers. match_ransac performs RANSAC, which selects random 4 points, calculate H, and get Euclidean distance between warped source points and reference points. While iterating over 1000 times, save the best results and returns Homography matrix.

After finding Homography matrix, need perspective projection of image plane. Backward warping use inverse mapping between reference image coordinate(x',y') and source coordinage(x,y). This makes every pixel of reference image mapping into source coordinate, preventing holes. Backward mapping is implemented in warp function, shown below.

# Backward warping은 output의 좌표에 대응되는 값을 source에서 찾는다
    # 이로 인해, output에서는 black hole들이 생기지 않는다는 장점이 있다
    for x in range(size_x): # ouput의 x좌표
        for y in range(size_y): # ouput의 y좌표
            # Inverse Homography matrix를 이용하여 
            point_xy = homogeneous_coordinate(np.dot(homography_inverse, [[x+ offset_x], [y+offset_y], [1]]))
            point_x = int(point_xy[0]) # source의 x좌표
            point_y = int(point_xy[1]) # source의 y좌표
            if (point_x >= 0 and point_x < column_number and point_y >= 0 and point_y < row_number): # output 영역 안에서만 정의
                result[y, x, :] = image_array[point_y, point_x, :]

blend3images performs mosaicing images with homography matrices found above.

Before Stitching

After Stitching

Before Stitching

After Stitching

Before Stitching

After Stitching