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%matplotlib inline
from __future__ import division, print_function
Enhanced from the original demo as featured in the scikit-image paper. This version does not require Enblend, instead stitching images along minimum-cost paths.
This notebook may be found at https://github.com/scikit-image/scikit-image-demos
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import numpy as np
import matplotlib.pyplot as plt
from skimage import io
def compare(*images, **kwargs):
"""
Utility function to display images side by side.
Parameters
----------
image0, image1, image2, ... : ndarrray
Images to display.
labels : list
Labels for the different images.
"""
f, axes = plt.subplots(1, len(images), **kwargs)
axes = np.array(axes, ndmin=1)
labels = kwargs.pop('labels', None)
if labels is None:
labels = [''] * len(images)
for n, (image, label) in enumerate(zip(images, labels)):
axes[n].imshow(image, interpolation='nearest', cmap='gray')
axes[n].set_title(label)
axes[n].axis('off')
plt.tight_layout()
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pano_imgs = io.ImageCollection('data/JDW_9*')
Inspect these images using the convenience function defined earlier
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compare(*pano_imgs, figsize=(15, 10))
Credit: Images of Private Arch and the trail to Delicate Arch in Arches National Park, USA, taken by Joshua D. Warner.
License: CC-BY 4.0
This stage usually involves one or more of the following:
For convenience our example data is already resized smaller, and we won't bother cropping. However, they are presently in color so coversion to grayscale with skimage.color.rgb2gray is appropriate.
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from skimage.color import rgb2gray
pano0 = rgb2gray(pano_imgs[0])
pano1 = rgb2gray(pano_imgs[1])
pano2 = rgb2gray(pano_imgs[2])
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# View the results
compare(pano0, pano1, pano2, figsize=(15, 10))
We need to estimate a projective transformation that relates these images together. The steps will be
In this three-shot series, the middle image pano1 is the logical anchor point.
We detect "Oriented FAST and rotated BRIEF" (ORB) features in both images.
Note: For efficiency in this tutorial we're only finding 400 keypoints. The results are good but have small variations. If you wanted a more robust estimate in practice, run multiple times and pick the best result or generate additional keypoints.
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from skimage.feature import ORB
# Initialize ORB
# 800 keypoints is large enough for robust results,
# but low enough to run within a few seconds.
orb = ORB(n_keypoints=800, fast_threshold=0.05)
# Detect keypoints in pano0
orb.detect_and_extract(pano0)
keypoints0 = orb.keypoints
descriptors0 = orb.descriptors
# Detect keypoints in pano1
orb.detect_and_extract(pano1)
keypoints1 = orb.keypoints
descriptors1 = orb.descriptors
# Detect keypoints in pano2
orb.detect_and_extract(pano2)
keypoints2 = orb.keypoints
descriptors2 = orb.descriptors
Match features from images 0 <-> 1 and 1 <-> 2.
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from skimage.feature import match_descriptors
# Match descriptors between left/right images and the center
matches01 = match_descriptors(descriptors0, descriptors1, cross_check=True)
matches12 = match_descriptors(descriptors1, descriptors2, cross_check=True)
Inspect these matched features side-by-side using the convenience function skimage.feature.plot_matches.
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from skimage.feature import plot_matches
fig, ax = plt.subplots(1, 1, figsize=(15, 12))
# Best match subset for pano0 -> pano1
plot_matches(ax, pano0, pano1, keypoints0, keypoints1, matches01)
ax.axis('off');
Most of these line up similarly, but it isn't perfect. There are a number of obvious outliers or false matches.
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fig, ax = plt.subplots(1, 1, figsize=(15, 12))
# Best match subset for pano2 -> pano1
plot_matches(ax, pano1, pano2, keypoints1, keypoints2, matches12)
ax.axis('off');
Similar to above, decent signal but numerous false matches.
To filter out the false matches, we apply RANdom SAMple Consensus (RANSAC), a powerful method of rejecting outliers available in skimage.transform.ransac. The transformation is estimated using an iterative process based on randomly chosen subsets, finally selecting the model which corresponds best with the majority of matches.
We need to do this twice, once each for the transforms from left -> center and right -> center.
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from skimage.transform import ProjectiveTransform
from skimage.measure import ransac
# Select keypoints from
# * source (image to be registered): pano0
# * target (reference image): pano1, our middle frame registration target
src = keypoints0[matches01[:, 0]][:, ::-1]
dst = keypoints1[matches01[:, 1]][:, ::-1]
model_robust01, inliers01 = ransac((src, dst), ProjectiveTransform,
min_samples=4, residual_threshold=1, max_trials=300)
# Select keypoints from
# * source (image to be registered): pano2
# * target (reference image): pano1, our middle frame registration target
src = keypoints2[matches12[:, 1]][:, ::-1]
dst = keypoints1[matches12[:, 0]][:, ::-1]
model_robust12, inliers12 = ransac((src, dst), ProjectiveTransform,
min_samples=4, residual_threshold=1, max_trials=300)
The inliers returned from RANSAC select the best subset of matches. How do they look?
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fig, ax = plt.subplots(1, 1, figsize=(15, 12))
# Best match subset for pano0 -> pano1
plot_matches(ax, pano0, pano1, keypoints0, keypoints1, matches01[inliers01])
ax.axis('off');
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fig, ax = plt.subplots(1, 1, figsize=(15, 12))
# Best match subset for pano2 -> pano1
plot_matches(ax, pano1, pano2, keypoints1, keypoints2, matches12[inliers12])
ax.axis('off');
Most of the false matches are rejected!
Next, we want to produce the panorama itself. To do that, we must warp, or transform, two of the three images so they will properly align with the stationary image.
The first step is to find the shape of the output image required to contain all three transformed images. To do this we consider the extents of all warped images.
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from skimage.transform import SimilarityTransform
# Shape of middle image, our registration target
r, c = pano1.shape[:2]
# Note that transformations take coordinates in (x, y) format,
# not (row, column), in order to be consistent with most literature
corners = np.array([[0, 0],
[0, r],
[c, 0],
[c, r]])
# Warp the image corners to their new positions
warped_corners01 = model_robust01(corners)
warped_corners12 = model_robust12(corners)
# Find the extents of both the reference image and the warped
# target image
all_corners = np.vstack((warped_corners01, warped_corners12, corners))
# The overally output shape will be max - min
corner_min = np.min(all_corners, axis=0)
corner_max = np.max(all_corners, axis=0)
output_shape = (corner_max - corner_min)
# Ensure integer shape with np.ceil and dtype conversion
output_shape = np.ceil(output_shape[::-1]).astype(int)
Warp the images with skimage.transform.warp according to the estimated transformation model. A shift, or translation is necessary as our middle image needs to be placed in the middle, so it isn't truly stationary.
Values outside the input images are set to -1 to distinguish the "background", which is identified for later use.
Note: warp takes the inverse mapping as an input.
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from skimage.transform import warp
# This in-plane offset is the only necessary transformation for the middle image
offset1 = SimilarityTransform(translation= -corner_min)
# Warp pano0 to pano1 using 3rd order interpolation
transform01 = (model_robust01 + offset1).inverse
pano0_warped = warp(pano0, transform01, order=3,
output_shape=output_shape, cval=-1)
pano0_mask = (pano0_warped != -1) # Mask == 1 inside image
pano0_warped[~pano0_mask] = 0 # Return background values to 0
# Translate pano1 into place
pano1_warped = warp(pano1, offset1.inverse, order=3,
output_shape=output_shape, cval=-1)
pano1_mask = (pano1_warped != -1) # Mask == 1 inside image
pano1_warped[~pano1_mask] = 0 # Return background values to 0
# Warp pano2 on to pano1
transform12 = (model_robust12 + offset1).inverse
pano2_warped = warp(pano2, transform12, order=3,
output_shape=output_shape, cval=-1)
pano2_mask = (pano2_warped != -1) # Mask == 1 inside image
pano2_warped[~pano2_mask] = 0 # Return background values to 0
Inspect the warped images:
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compare(pano0_warped, pano1_warped, pano2_warped, figsize=(15, 10));
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# Add the three images together. This could create dtype overflows!
# We know they are are floating point images after warping, so it's OK.
merged = (pano0_warped + pano1_warped + pano2_warped)
# Track the overlap by adding the masks together
overlap = (pano0_mask * 1.0 + # Multiply by 1.0 for bool -> float conversion
pano1_mask +
pano2_mask)
# Normalize through division by `overlap` - but ensure the minimum is 1
normalized = merged / np.maximum(overlap, 1)
Finally, view the results!
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fig, ax = plt.subplots(figsize=(15, 12))
ax.imshow(normalized, cmap='gray')
plt.tight_layout()
ax.axis('off');
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What happened?! Why are there nasty dark lines at boundaries, and why does the middle look so blurry?
This is an artifact (boundary effect) from the warping method. When the image is warped with interpolation, the edge values are affected by the background. We could have bright lines if we'd chosen cval=1 in the warp calls, but regardless of choice there will always be discontinuities.
...Unless you use order=0 in warp, which is nearest neighbor. Then these edges are perfect (try it!). But who wants to be limited to an inferior interpolation method? And, even then, it's blurry! Isn't there a better way?
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fig, ax = plt.subplots(figsize=(15,12))
# Generate difference image and inspect it
difference_image = pano0_warped - pano1_warped
ax.imshow(difference_image, cmap='gray')
ax.axis('off');
The surrounding flat gray is zero, so we see the overlap region matches fairly well in the middle... but off to the sides where things start to look a little embossed, a simple average would blur the result. Indeed it did when we averaged everything (look again at the previous averaged panorama). This is almost always the case for panoramas!
So, perhaps a different approach is needed?
Let's attempt to find a vertical path through this difference image which stays as close to zero as possible. If we use that to build a mask, defining a transition between images, the result should appear seamless.
skimage.graphThe skimage.graph submodule allows you to start at any point on an array, and find the path to any other point which will minimize the sum of values on the path.
The overarching array is called a cost array, while the path found is a minimum-cost path or MCP.
To accomplish this we need
This method is so powerful that, with a carefully constructed costs array, the seed points are essentially irrelevant. It just works!
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ymax = output_shape[1] - 1
xmax = output_shape[0] - 1
# Start anywhere along the top and bottom, left of center.
mask_pts01 = [[0, ymax // 3],
[xmax, ymax // 3]]
# Start anywhere along the top and bottom, right of center.
mask_pts12 = [[0, 2*ymax // 3],
[xmax, 2*ymax // 3]]
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from skimage.measure import label
def generate_costs(diff_image, mask, vertical=True, gradient_cutoff=2.):
"""
Ensures equal-cost paths from edges to region of interest.
Parameters
----------
diff_image : ndarray of floats
Difference of two overlapping images.
mask : ndarray of bools
Mask representing the region of interest in ``diff_image``.
vertical : bool
Control operation orientation.
gradient_cutoff : float
Controls how far out of parallel lines can be to edges before
correction is terminated. The default (2.) is good for most cases.
Returns
-------
costs_arr : ndarray of floats
Adjusted costs array, ready for use.
"""
if vertical is not True:
return tweak_costs(diff_image.T, mask.T, vertical=vertical,
gradient_cutoff=gradient_cutoff).T
# Start with a high-cost array of 1's
costs_arr = np.ones_like(diff_image)
# Obtain extent of overlap
row, col = mask.nonzero()
cmin = col.min()
cmax = col.max()
# Label discrete regions
cslice = slice(cmin, cmax + 1)
labels = label(mask[:, cslice])
# Find distance from edge to region
upper = (labels == 0).sum(axis=0)
lower = (labels == 2).sum(axis=0)
# Reject areas of high change
ugood = np.abs(np.gradient(upper)) < gradient_cutoff
lgood = np.abs(np.gradient(lower)) < gradient_cutoff
# Give areas slightly farther from edge a cost break
costs_upper = np.ones_like(upper, dtype=np.float64)
costs_lower = np.ones_like(lower, dtype=np.float64)
costs_upper[ugood] = upper.min() / np.maximum(upper[ugood], 1)
costs_lower[lgood] = lower.min() / np.maximum(lower[lgood], 1)
# Expand from 1d back to 2d
vdist = mask.shape[0]
costs_upper = costs_upper[np.newaxis, :].repeat(vdist, axis=0)
costs_lower = costs_lower[np.newaxis, :].repeat(vdist, axis=0)
# Place these in output array
costs_arr[:, cslice] = costs_upper * (labels == 0)
costs_arr[:, cslice] += costs_lower * (labels == 2)
# Finally, place the difference image
costs_arr[mask] = diff_image[mask]
return costs_arr
Next we use this function to generate the cost array. We will start with the difference, but must modify it further or it will take the trivial path around either image, as the background is all zeros!
We also set the top and bottom edges to be zero, so our path can freely slide to the optimal vertical path.
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# Start with the absolute value of the difference image.
# np.abs is necessary because we don't want negative costs!
costs01 = generate_costs(np.abs(pano0_warped - pano1_warped),
pano0_mask & pano1_mask)
Allow the path to "slide" along top and bottom edges to the optimal horizontal position by setting top and bottom edges to zero cost.
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costs01[0, :] = 0
costs01[-1, :] = 0
Our costs array now looks like this
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fig, ax = plt.subplots(figsize=(8, 8))
ax.imshow(costs01, cmap='gray');
The tweak we made with generate_costs is subtle but important.
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from skimage.graph import route_through_array
# Arguments are:
# cost array
# start pt
# end pt
# can it traverse diagonally
pts, _ = route_through_array(costs01, mask_pts01[0], mask_pts01[1], fully_connected=True)
# Convert list of lists to 2d coordinate array for easier indexing
pts = np.array(pts)
Let's see how it worked
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fig, ax = plt.subplots(figsize=(15, 15))
# Plot the difference image
ax.imshow(pano0_warped - pano1_warped, cmap='gray')
# Overlay the minimum-cost path
ax.plot(pts[:, 1], pts[:, 0])
plt.tight_layout()
ax.axis('off');
That looks like a great seam to stitch these images together - the entire path looks very close to zero.
Due to the random element in the RANSAC transform estimation, everyone will have a slightly different path. Your path will look different from mine, and different from your neighbor's. That's intended! The awesome thing about MCP is that everyone just calculated the best possible path to stitch together their unique transforms!
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# Start with an array of zeros and place the path
mask0 = np.zeros_like(pano0_warped, dtype=np.uint8)
mask0[pts[:, 0], pts[:, 1]] = 1
Ensure the path appears as expected
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fig, ax = plt.subplots(figsize=(11, 11))
# View the path in black and white
ax.imshow(mask0, cmap='gray')
ax.axis('off');
Label the various contiguous regions in the image using skimage.measure.label
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from skimage.measure import label
# Labeling starts with zero at point (0, 0)
mask0[label(mask0, connectivity=1) == 0] = 1
# The result
plt.imshow(mask0, cmap='gray');
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# Start with the absolute value of the difference image.
# np.abs necessary because we don't want negative costs!
costs12 = generate_costs(np.abs(pano1_warped - pano2_warped),
pano1_mask & pano2_mask)
# Allow the path to "slide" along top and bottom edges to the optimal
# horizontal position by setting top and bottom edges to zero cost
costs12[0, :] = 0
costs12[-1, :] = 0
Add an additional constraint this time, to prevent this path crossing the prior one!
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costs12[mask0 > 0] = 1
Check the result
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fig, ax = plt.subplots(figsize=(8, 8))
ax.imshow(costs12, cmap='gray');
Your results may look slightly different.
Compute the minimal cost path
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# Arguments are:
# cost array
# start pt
# end pt
# can it traverse diagonally
pts, _ = route_through_array(costs12, mask_pts12[0], mask_pts12[1], fully_connected=True)
# Convert list of lists to 2d coordinate array for easier indexing
pts = np.array(pts)
Verify a reasonable result
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fig, ax = plt.subplots(figsize=(15, 15))
# Plot the difference image
ax.imshow(pano1_warped - pano2_warped, cmap='gray')
# Overlay the minimum-cost path
ax.plot(pts[:, 1], pts[:, 0]);
ax.axis('off');
Initialize the mask by placing the path in a new array
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mask2 = np.zeros_like(pano0_warped, dtype=np.uint8)
mask2[pts[:, 0], pts[:, 1]] = 1
Fill the right side this time, again using skimage.measure.label - the label of interest is 2
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mask2[label(mask2, connectivity=1) == 2] = 1
# The result
plt.imshow(mask2, cmap='gray');
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mask1 = ~(mask0 | mask2).astype(bool)
Define a convenience function to place masks in alpha channels
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def add_alpha(img, mask=None):
"""
Adds a masked alpha channel to an image.
Parameters
----------
img : (M, N[, 3]) ndarray
Image data, should be rank-2 or rank-3 with RGB channels
mask : (M, N[, 3]) ndarray, optional
Mask to be applied. If None, the alpha channel is added
with full opacity assumed (1) at all locations.
"""
from skimage.color import gray2rgb
if mask is None:
mask = np.ones_like(img)
if img.ndim == 2:
img = gray2rgb(img)
return np.dstack((img, mask))
Obtain final, alpha blended individual images and inspect them
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pano0_final = add_alpha(pano0_warped, mask0)
pano1_final = add_alpha(pano1_warped, mask1)
pano2_final = add_alpha(pano2_warped, mask2)
compare(pano0_final, pano1_final, pano2_final, figsize=(15, 15))
What we have here is the world's most complicated and precisely-fitting jigsaw puzzle...
Plot all three together and view the results!
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fig, ax = plt.subplots(figsize=(15, 12))
# This is a perfect combination, but matplotlib's interpolation
# makes it appear to have gaps. So we turn it off.
ax.imshow(pano0_final, interpolation='none')
ax.imshow(pano1_final, interpolation='none')
ax.imshow(pano2_final, interpolation='none')
fig.tight_layout()
ax.axis('off');
Fantastic! Without the black borders, you'd never know this was composed of separate images!
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# Identical transforms as before, except
# * Operating on original color images
# * filling with cval=0 as we know the masks
pano0_color = warp(pano_imgs[0], (model_robust01 + offset1).inverse, order=3,
output_shape=output_shape, cval=0)
pano1_color = warp(pano_imgs[1], offset1.inverse, order=3,
output_shape=output_shape, cval=0)
pano2_color = warp(pano_imgs[2], (model_robust12 + offset1).inverse, order=3,
output_shape=output_shape, cval=0)
Then apply the custom alpha channel masks
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pano0_final = add_alpha(pano0_color, mask0)
pano1_final = add_alpha(pano1_color, mask1)
pano2_final = add_alpha(pano2_color, mask2)
View the result!
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fig, ax = plt.subplots(figsize=(15, 12))
# Turn off matplotlib's interpolation
ax.imshow(pano0_final, interpolation='none')
ax.imshow(pano1_final, interpolation='none')
ax.imshow(pano2_final, interpolation='none')
fig.tight_layout()
ax.axis('off');
Save the combined, color panorama locally as './pano-advanced-output.png'
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from skimage.color import gray2rgb
# Start with empty image
pano_combined = np.zeros_like(pano0_color)
# Place the masked portion of each image into the array
# masks are 2d, they need to be (M, N, 3) to match the color images
pano_combined += pano0_color * gray2rgb(mask0)
pano_combined += pano1_color * gray2rgb(mask1)
pano_combined += pano2_color * gray2rgb(mask2)
# Save the output - precision loss warning is expected
# moving from floating point -> uint8
io.imsave('./pano-advanced-output.png', pano_combined)
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Go back to the top. Under "Load Data" replace the string 'data/JDW_03*' with 'data/JDW_9*', and re-run all of the cells in order.
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