Added HW3.zip and README.md Edited

Signed-off-by: Vaishnav Murali <vaishnavmurali@gmail.com>

Author: vaishnavm217

Assignment-3/HW3.zip

@@ -1,10 +1,11 @@
 import cv2
 import numpy as np
+import numpy
 import matplotlib.pyplot as plt
 import sys
 import random
-from scipy.sparse.linalg import svds
-from sklearn import linear_model
+NN_THRESHOLD = 0.7
+PIXEL_ERROR_THRESHOLD = 3
 Detector = cv2.xfeatures2d.SIFT_create()
 def SIFT(image):
  return Detector.detectAndCompute(image,None)
@@ -16,7 +17,7 @@ def matches(feature1,feature2,kp1,kp2):
  features2 = []
  for k,i in enumerate(feature2):
  ind = np.argsort(np.linalg.norm(np.subtract(feature1,i),axis=1))[:2]
- if np.linalg.norm(i-feature1[ind[0]])< 0.7 * np.linalg.norm(i-feature1[ind[1]]): #ratio : 0.7-0.8
+ if np.linalg.norm(i-feature1[ind[0]])< NN_THRESHOLD * np.linalg.norm(i-feature1[ind[1]]): #ratio : 0.7-0.8
  kps2.append(kp2[k])
  features2.append(i)
  kps1.append(kp1[ind[0]])
@@ -41,6 +42,7 @@ def merge_images():
  ptA = (int(kps1[i].pt[0]), int(kps1[i].pt[1]))
  ptB = (int(kps2[i].pt[0]) + wA, int(kps2[i].pt[1]))
  cv2.line(vis, ptA, ptB, (random.randint(0,255), random.randint(0,255), random.randint(0,255)), 1)
+ plt.imsave("Matches.jpg",vis)
  plt.title("Matches")
  plt.imshow(vis)
  kps1 = np.array(kps1)
@@ -56,30 +58,56 @@ def merge_images():
  best_count = -1
  for i in range(len(kps1)):
  ind = np.array(random.sample(list(range(len(kps1))),4))
- x_p = np.array([[v.pt[0],v.pt[1]] for v in kps1[ind]])
- x = np.array([[v.pt[0],v.pt[1]] for v in kps2[ind]])
+ x_p = np.array([[v.pt[0],v.pt[1],1] for v in kps1[ind]])
+ x = np.array([[v.pt[0],v.pt[1],1] for v in kps2[ind]])
  A = np.array([])
- for j in range(4):
- A = np.vstack([A,
- [[-x[j,0],-x[j,1],-1,0,0,0,x[j,0]*x_p[j,0],x[j,1]*x_p[j,0],x_p[j,0]],
- [0,0,0,-x[j,0],-x[j,1],-1,x[j,0]*x_p[j,1],x[j,1]*x_p[j,1],x_p[j,1]]]]
- ) if A.size else np.array([[-x[j,0],-x[j,1],-1,0,0,0,x[j,0]*x_p[j,0],x[j,1]*x_p[j,0],x_p[j,0]],[0,0,0,-x[j,0],-x[j,1],-1,x[j,0]*x_p[j,1],x[j,1]*x_p[j,1],x_p[j,1]]])
- u,s,vh = np.linalg.svd(A)
- xtemp = np.hstack([x_p,np.ones((x.shape[0],1))])
- xori = np.hstack([x,np.ones((x_p.shape[0],1))])
- L = vh[-1,:]
- h = L.reshape((3,3))
+ fp = x
+ tp = x_p
+ m = numpy.mean(fp[:2], axis=1)
+ maxstd = numpy.max(numpy.std(fp[:2], axis=1)) + 1e-9
+ C1 = numpy.diag([1/maxstd, 1/maxstd, 1])
+ C1[0, 2] = -m[0] / maxstd
+ C1[1, 2] = -m[1] / maxstd
+ fp = numpy.dot(C1, fp.T)
+
+ # -to
+ m = numpy.mean(tp[:2], axis=1)
+ maxstd = numpy.max(numpy.std(tp[:2], axis=1)) + 1e-9
+ C2 = numpy.diag([1/maxstd, 1/maxstd, 1])
+ C2[0, 2] = -m[0] / maxstd
+ C2[1, 2] = -m[1] / maxstd
+ tp = numpy.dot(C2, tp.T)
+
+ correspondences_count = fp.shape[1]
+ A = numpy.zeros((2 * correspondences_count, 9))
+ for i in range(correspondences_count):
+ A[2 * i ] = [-fp[0][i], -fp[1][i], -1, 0, 0, 0,
+ tp[0][i] * fp[0][i], tp[0][i] * fp[1][i], tp[0][i]]
+ A[2 * i + 1] = [0, 0, 0, -fp[0][i], -fp[1][i], -1,
+ tp[1][i] * fp[0][i], tp[1][i] * fp[1][i], tp[1][i]]
+
+ U, S, V = numpy.linalg.svd(A)
+ H = V[8].reshape((3, 3))
+
+ H = numpy.dot(numpy.linalg.inv(C2), numpy.dot(H, C1))
+ h = H/H[2,2]
  homo_x = np.matmul(h,kp2_coordinates.T)
- k = np.linalg.norm(kp1_coordinates-homo_x.T,axis=1)<3
+ k = np.linalg.norm(kp1_coordinates-homo_x.T,axis=1)<PIXEL_ERROR_THRESHOLD
  if best_count<np.count_nonzero(k):
  best_count = np.count_nonzero(k)
  best_h = h
- # print(best_count)
+ # return H / H[2, 2]
+
+
+
+ print(best_count)
  result = cv2.warpPerspective(img2,best_h,
 	(img1.shape[1] + img2.shape[1], img1.shape[0]))
+ plt.imsave("Homography.jpg",result)
  result[0:img1.shape[0],0:img2.shape[1]] = img1
+ plt.imsave("Result.jpg",result)
 
- H,mask = cv2.findHomography(kp2_coordinates, kp1_coordinates, cv2.RANSAC,5.0)
+ H,mask = cv2.findHomography(kp2_coordinates, kp1_coordinates, cv2.RANSAC,PIXEL_ERROR_THRESHOLD)
  result1 = cv2.warpPerspective(img2,H,
 	(img1.shape[1] + img2.shape[1], img1.shape[0]))
  result1[0:img1.shape[0],0:img2.shape[1]] = img1

Assignment-3/Q1/Q1.py

@@ -1 +1,29 @@
 # Q3: Image Stitching
+#### Usage:
+```bash
+$ python Q3.py
+```
+### Note:
+- The program assumes `uttower_right.jpg` and `uttower_left.jpg` are in the same folder.
+- It has Thresholds hardcoded in it. Please change according to your needs for any modification.
+- As the program uses SIFT descriptor, the original cv2 won't have this (SIFT is proprietary). To run the code, uninstall cv2 using
+```
+pip uninstall opencv-python
+```
+and install `opencv-python-contrib` by running
+```
+pip install opencv-python-contrib
+```
+
+### Report
+First the SIFT descriptor matches are found based on the Nearest Neighbour with a threshold distance as mentioned in [David Lowe's Paper](https://people.eecs.berkeley.edu/~malik/cs294/lowe-ijcv04.pdf)
+![Matches](Matches.jpg)
+
+The Homography Matrix is selected using RANSAC and DLT, which selects the matrix which projects the maximum number of matches within a threhold.
+This generates a warped image in the final image plane using the found Homography.
+![Warped Perspective](Homography.jpg)
+
+The Left image is overwritten in the warped image (no blending used)
+![Result](Result.jpg)
+
+As RANSAC is used, this might not generate same images every time, But will have decent merged images.