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POHow can I transform an image so that projected image is same as original
 

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  1. POHow can I transform an image so that projected image is same as original
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    <p>Problem statement: An image A is projected through a projector, goes through a microscope and the projected image is captured via a camera through the same microscope as image B. Due to the optical elements, the B is rotated, sheared and distorted with respect to A. Now, I need to transform A into A' before projection such that B is as close to A as possible.</p> <p>Initial approach: I took a checkerboard pattern and rotated it at various angles (36, 72, 108, ... 324 degrees) and projected to get a series of A images and B images. I used OpenCV's CalibrateCamera2, InitUndistortMap and Remap functions to convert B into B'. But B' is nowhere near A and rather similar to B (especially there is a significant amount of rotation and shearing that is not getting corrected).</p> <p>The code (in Python) is below. I am not sure if I am doing something stupid. Any ideas for the correct approach?</p> <pre><code>import pylab import os import cv import cv2 import numpy # angles - the angles at which the picture was rotated angles = [0, 36, 72, 108, 144, 180, 216, 252, 288, 324] # orig_files - list of original picture files used for projection orig_files = ['../calibration/checkerboard/orig_%d.png' % (angle) for angle in angles] # img_files - projected image captured by camera img_files = ['../calibration/checkerboard/imag_%d.bmp' % (angle) for angle in angles] # Load the images images = [cv.LoadImage(filename) for filename in img_files] orig_images = [cv.LoadImage(filename) for filename in orig_files] # Convert to grayscale gray_images = [cv.CreateImage((src.height, src.width), cv.IPL_DEPTH_8U, 1) for src in images] for ii in range(len(images)): cv.CvtColor(images[ii], gray_images[ii], cv.CV_RGB2GRAY) gray_orig = [cv.CreateImage((src.height, src.width), cv.IPL_DEPTH_8U, 1) for src in orig_images] for ii in range(len(orig_images)): cv.CvtColor(orig_images[ii], gray_orig[ii], cv.CV_RGB2GRAY) # The number of ranks and files in the chessboard. OpenCV considers # the height and width of the chessboard to be one less than these, # respectively. rank_count = 11 file_count = 10 # Try to detect the corners of the chessboard. For each image, # FindChessboardCorners returns (found, corner_points). found is True # even if it managed to detect only a subset of the actual corners. img_corners = [cv.FindChessboardCorners(img, (rank_count-1, file_count-1)) for img in gray_images] orig_corners = [cv.FindChessboardCorners(img, (rank_count-1,file_count-1)) for img in gray_orig] # The total number of corners will be (rank_count-1)x(file_count-1), # but if some parts of the image are too blurred/distorted, # FindChessboardCorners detects only a subset of the corners. In that # case, DrawChessboardCorners will raise a TypeError. orig_corner_success = [] ii = 0 for (found, corners) in orig_corners: if found and (len(corners) == (rank_count - 1) * (file_count - 1)): orig_corner_success.append(ii) else: print orig_files[ii], ': could not find correct corners: ', len(corners) ii += 1 ii = 0 img_corner_success = [] for (found, corners) in img_corners: if found and (len(corners) == (rank_count-1) * (file_count-1)) and (ii in orig_corner_success): img_corner_success.append(ii) else: print img_files[ii], ': Number of corners detected is wrong:', len(corners) ii += 1 # Here we compile all the corner coordinates into single arrays image_points = [] obj_points = [] for ii in img_corner_success: obj_points.extend(orig_corners[ii][1]) image_points.extend(img_corners[ii][2]) image_points = cv.fromarray(numpy.array(image_points, dtype='float32')) obj_points = numpy.hstack((numpy.array(obj_points, dtype='float32'), numpy.zeros((len(obj_points), 1), dtype='float32'))) obj_points = cv.fromarray(numpy.array(obj_points, order='C')) point_counts = numpy.ones((len(img_corner_success), 1), dtype='int32') * ((rank_count-1) * (file_count-1)) point_counts = cv.fromarray(point_counts) # Create the output parameters cam_mat = cv.CreateMat(3, 3, cv.CV_32FC1) cv.Set2D(cam_mat, 0, 0, 1.0) cv.Set2D(cam_mat, 1, 1, 1.0) dist_mat = cv.CreateMat(5, 1, cv.CV_32FC1) rot_vecs = cv.CreateMat(len(img_corner_success), 3, cv.CV_32FC1) tran_vecs = cv.CreateMat(len(img_corner_success), 3, cv.CV_32FC1) # Do the camera calibration x = cv.CalibrateCamera2(obj_points, image_points, point_counts, cv.GetSize(gray_images[0]), cam_mat, dist_mat, rot_vecs, tran_vecs) # Create the undistortion map xmap = cv.CreateImage(cv.GetSize(images[0]), cv.IPL_DEPTH_32F, 1) ymap = cv.CreateImage(cv.GetSize(images[0]), cv.IPL_DEPTH_32F, 1) cv.InitUndistortMap(cam_mat, dist_mat, xmap, ymap) # Now undistort all the images and same them ii = 0 for tmp in images: print img_files[ii] image = cv.GetImage(tmp) t = cv.CloneImage(image) cv.Remap(t, image, xmap, ymap, cv.CV_INTER_LINEAR + cv.CV_WARP_FILL_OUTLIERS, cv.ScalarAll(0)) corrected_file = os.path.join(os.path.dirname(img_files[ii]), 'corrected_%s' % (os.path.basename(img_files[ii]))) cv.SaveImage(corrected_file, image) print 'Saved corrected image to', corrected_file ii += 1 </code></pre> <p>Here are the images - A, B and B' Actually I don't think the Remap is really doing anything!</p> <p><img src="https://i.stack.imgur.com/epzn4.png" alt="A. Original Image"> <img src="https://i.stack.imgur.com/vypry.png" alt="B. Captured Image"> <img src="https://i.stack.imgur.com/zsNgz.png" alt="B&#39;. Undistorted Image"></p>
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      1. POHow can I transform an image so that projected image is same as original
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    1. CODo you know the entire optical setup? If you do you could write the matrix equation of the projection and calculate the inverse on the resulting image. This goes along [these lines](http://en.wikipedia.org/wiki/Ray_transfer_matrix_analysis).
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    2. COposting a sample image would be more illustrative. as in how close is your B to B'.
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    3. CO@Bort - no it is not possible to know the entire setup: the microscope's focus can be changed everytime.
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