Performing linear stack alignment with SIFT by python

Question

I want to perform the linear alignment with SIFT by using python.

I have found a possible method at How do I use the relationships between Flann matches to determine a sensible homography?

the code is:

# 2017.11.11 01:44:37 CST
# 2017.11.12 00:09:14 CST
"""
使用Sift特征点检测和匹配查找场景中特定物体。
"""

import cv2
import numpy as np
MIN_MATCH_COUNT = 4

imgname1 = "box.png"
imgname2 = "box_in_scene.png"

## (1) prepare data
img1 = cv2.imread(imgname1)
img2 = cv2.imread(imgname2)
gray1 = cv2.cvtColor(img1, cv2.COLOR_BGR2GRAY)
gray2 = cv2.cvtColor(img2, cv2.COLOR_BGR2GRAY)


## (2) Create SIFT object
sift = cv2.xfeatures2d.SIFT_create()

## (3) Create flann matcher
matcher = cv2.FlannBasedMatcher(dict(algorithm = 1, trees = 5), {})

## (4) Detect keypoints and compute keypointer descriptors
kpts1, descs1 = sift.detectAndCompute(gray1,None)
kpts2, descs2 = sift.detectAndCompute(gray2,None)

## (5) knnMatch to get Top2
matches = matcher.knnMatch(descs1, descs2, 2)
# Sort by their distance.
matches = sorted(matches, key = lambda x:x[0].distance)

## (6) Ratio test, to get good matches.
good = [m1 for (m1, m2) in matches if m1.distance < 0.7 * m2.distance]

canvas = img2.copy()

## (7) find homography matrix
## 当有足够的健壮匹配点对（至少4个）时
if len(good)>MIN_MATCH_COUNT:
    ## 从匹配中提取出对应点对
    ## (queryIndex for the small object, trainIndex for the scene )
    src_pts = np.float32([ kpts1[m.queryIdx].pt for m in good ]).reshape(-1,1,2)
    dst_pts = np.float32([ kpts2[m.trainIdx].pt for m in good ]).reshape(-1,1,2)
    ## find homography matrix in cv2.RANSAC using good match points
    M, mask = cv2.findHomography(src_pts, dst_pts, cv2.RANSAC,5.0)
    ## 掩模，用作绘制计算单应性矩阵时用到的点对
    #matchesMask2 = mask.ravel().tolist()
    ## 计算图1的畸变，也就是在图2中的对应的位置。
    h,w = img1.shape[:2]
    pts = np.float32([ [0,0],[0,h-1],[w-1,h-1],[w-1,0] ]).reshape(-1,1,2)
    dst = cv2.perspectiveTransform(pts,M)
    ## 绘制边框
    cv2.polylines(canvas,[np.int32(dst)],True,(0,255,0),3, cv2.LINE_AA)
else:
    print( "Not enough matches are found - {}/{}".format(len(good),MIN_MATCH_COUNT))


## (8) drawMatches
matched = cv2.drawMatches(img1,kpts1,canvas,kpts2,good,None)#,**draw_params)

## (9) Crop the matched region from scene
h,w = img1.shape[:2]
pts = np.float32([ [0,0],[0,h-1],[w-1,h-1],[w-1,0] ]).reshape(-1,1,2)
dst = cv2.perspectiveTransform(pts,M)
perspectiveM = cv2.getPerspectiveTransform(np.float32(dst),pts)
found = cv2.warpPerspective(img2,perspectiveM,(w,h))

## (10) save and display
cv2.imwrite("matched.png", matched)
cv2.imwrite("found.png", found)
cv2.imshow("matched", matched);
cv2.imshow("found", found);
cv2.waitKey();cv2.destroyAllWindows()

However, after performing the codes above, I found the alignment is nonlinear and the perspective transformation was applied in the final result. How can I revise the code to perform the linear alignment with SIFT? My final goal is to have the same performance as the plugin called "Linear stack alignment with SIFT" in FIJI(ImageJ).

If somebody knows the solution, please help me. Thanks in advance!