""" ======================================================= Diffeomorphic Registration with binary and fuzzy images ======================================================= This example demonstrates registration of a binary and a fuzzy image. This could be seen as aligning a fuzzy (sensed) image to a binary (e.g., template) image. """ import numpy as np import matplotlib.pyplot as plt from skimage import draw, filters from dipy.align.imwarp import SymmetricDiffeomorphicRegistration from dipy.align.metrics import SSDMetric from dipy.viz import regtools """ Let's generate a sample template image as the combination of three ellipses. We will generate the fuzzy (sensed) version of the image by smoothing the reference image. """ def draw_ellipse(img, center, axis): rr, cc = draw.ellipse(center[0], center[1], axis[0], axis[1], shape=img.shape) img[rr, cc] = 1 return img img_ref = np.zeros((64, 64)) img_ref = draw_ellipse(img_ref, (25, 15), (10, 5)) img_ref = draw_ellipse(img_ref, (20, 45), (15, 10)) img_ref = draw_ellipse(img_ref, (50, 40), (7, 15)) img_in = filters.gaussian(img_ref, sigma=3) """ Let's define a small visualization function. """ def show_images(img_ref, img_warp, fig_name): fig, axarr = plt.subplots(ncols=2, figsize=(12, 5)) axarr[0].set_title('warped image & reference contour') axarr[0].imshow(img_warp) axarr[0].contour(img_ref, colors='r') ssd = np.sum((img_warp - img_ref) ** 2) axarr[1].set_title('difference, SSD=%.02f' % ssd) im = axarr[1].imshow(img_warp - img_ref) plt.colorbar(im) fig.tight_layout() fig.savefig(fig_name + '.png') show_images(img_ref, img_in, 'input') """ .. figure:: input.png :align: center Input images before alignment. """ """ Let's use the general Registration function with some naive parameters, such as set `step_length` as 1 assuming maximal step 1 pixel and a reasonably small number of iterations since the deformation with already aligned images should be minimal. """ sdr = SymmetricDiffeomorphicRegistration(metric=SSDMetric(img_ref.ndim), step_length=1.0, level_iters=[50, 100], inv_iter=50, ss_sigma_factor=0.1, opt_tol=1.e-3) """ Perform the registration with equal images. """ mapping = sdr.optimize(img_ref.astype(float), img_ref.astype(float)) img_warp = mapping.transform(img_ref, 'linear') show_images(img_ref, img_warp, 'output-0') regtools.plot_2d_diffeomorphic_map(mapping, 5, 'map-0.png') """ .. figure:: output-0.png :align: center .. figure:: map-0.png :align: center Registration results for default parameters and equal images. """ """ Perform the registration with binary and fuzzy images. """ mapping = sdr.optimize(img_ref.astype(float), img_in.astype(float)) img_warp = mapping.transform(img_in, 'linear') show_images(img_ref, img_warp, 'output-1') regtools.plot_2d_diffeomorphic_map(mapping, 5, 'map-1.png') """ .. figure:: output-1.png :align: center .. figure:: map-1.png :align: center Registration results for a naive parameter configuration. """ """ Note, we are still using a multi-scale approach which makes `step_length` in the upper level multiplicatively larger. What happens if we set `step_length` to a rather small value? """ sdr.step_length = 0.1 """ Perform the registration and examine the output. """ mapping = sdr.optimize(img_ref.astype(float), img_in.astype(float)) img_warp = mapping.transform(img_in, 'linear') show_images(img_ref, img_warp, 'output-2') regtools.plot_2d_diffeomorphic_map(mapping, 5, 'map-2.png') """ .. figure:: output-2.png :align: center .. figure:: map-2.png :align: center Registration results for decreased step size. """ """ An alternative scenario is to use just a single-scale level. Even though the warped image may look fine, the estimated deformations show that it is off the mark. """ sdr = SymmetricDiffeomorphicRegistration(metric=SSDMetric(img_ref.ndim), step_length=1.0, level_iters=[100], inv_iter=50, ss_sigma_factor=0.1, opt_tol=1.e-3) """ Perform the registration. """ mapping = sdr.optimize(img_ref.astype(float), img_in.astype(float)) img_warp = mapping.transform(img_in, 'linear') show_images(img_ref, img_warp, 'output-3') regtools.plot_2d_diffeomorphic_map(mapping, 5, 'map-3.png') """ .. figure:: output-3.png :align: center .. figure:: map-3.png :align: center Registration results for single level. """