def refine_worm(image, initial_area, candidate_edges):
# find strong worm edges (roughly equivalent to the edges found by find_initial_worm,
# which are in candidate_edges): smooth the image, do canny edge-finding, and
# then keep only those edges near candidate_edges
smooth_image = restoration.denoise_tv_bregman(image, 140).astype(numpy.float32)
smoothed, gradient, sobel = canny.prepare_canny(smooth_image, 8, initial_area)
local_maxima = canny.canny_local_maxima(gradient, sobel)
candidate_edge_region = ndimage.binary_dilation(candidate_edges, iterations=4)
strong_edges = local_maxima & candidate_edge_region
# Now threshold the image to find dark blobs as our initial worm region
# First, find areas in the initial region unlikely to be worm pixels
mean, std = mcd.robust_mean_std(smooth_image[initial_area][::4], 0.85)
non_worm = (smooth_image > mean - std) & initial_area
# now fit a smoothly varying polynomial to the non-worm pixels in the initial
# region of interest, and subtract that from the actual image to generate
# an image with a flat illumination field
background = polyfit.fit_polynomial(smooth_image, mask=non_worm, degree=2)
minus_bg = smooth_image - background
# now recalculate a threshold from the background-subtracted pixels
mean, std = mcd.robust_mean_std(minus_bg[initial_area][::4], 0.85)
initial_worm = (minus_bg < mean - std) & initial_area
# Add any pixels near the strong edges to our candidate worm position
initial_worm |= ndimage.binary_dilation(strong_edges, iterations=3)
initial_worm = mask.fill_small_radius_holes(initial_worm, 5)
# Now grow/shrink the initial_worm region so that as many of the strong
# edges from the canny filter are in contact with the region edges as possible.
ac = active_contour.EdgeClaimingAdvection(initial_worm, strong_edges,
max_region_mask=initial_area)
stopper = active_contour.StoppingCondition(ac, max_iterations=100)
while stopper.should_continue():
ac.advect(iters=1)
ac.smooth(iters=1, depth=2)
worm_mask = mask.fill_small_radius_holes(ac.mask, 7)
# Now, get edges from the image at a finer scale
smoothed, gradient, sobel = canny.prepare_canny(smooth_image, 0.3, initial_area)
local_maxima = canny.canny_local_maxima(gradient, sobel)
strong_sum = strong_edges.sum()
highp = 100 * (1 - 1.5*strong_sum/local_maxima.sum())
lowp = max(100 * (1 - 3*strong_sum/local_maxima.sum()), 0)
low_worm, high_worm = numpy.percentile(gradient[local_maxima], [lowp, highp])
fine_edges = canny.canny_hysteresis(local_maxima, gradient, low_worm, high_worm)
# Expand out the identified worm area to include any of these finer edges
closed_edges = ndimage.binary_closing(fine_edges, structure=S)
worm = ndimage.binary_propagation(worm_mask, mask=worm_mask|closed_edges, structure=S)
worm = ndimage.binary_closing(worm, structure=S, iterations=2)
worm = mask.fill_small_radius_holes(worm, 5)
worm = ndimage.binary_opening(worm)
worm = mask.get_largest_object(worm)
# Last, smooth the shape a bit to reduce sharp corners, but not too much to
# sand off the tail
ac = active_contour.CurvatureMorphology(worm, max_region_mask=initial_area)
ac.smooth(depth=2, iters=2)
return strong_edges, ac.mask
def find_initial_worm(small_image, well_mask):
# plan here is to find known good worm edges with Canny using a stringent threshold, then
# relax the threshold in the vicinity of the good edges.
# back off another pixel from the well edge to avoid gradient from the edge
shrunk_mask = ndimage.binary_erosion(well_mask, structure=S)
smoothed, gradient, sobel = canny.prepare_canny(small_image, 2, shrunk_mask)
local_maxima = canny.canny_local_maxima(gradient, sobel)
# Calculate stringent and medium-stringent thresholds. The stringent threshold
# is the 200th-brightest edge pixel, and the medium is the 450th-brightest pixel
highp = 100 * (1-200/local_maxima.sum())
highp = max(highp, 94)
mediump = 100 * (1-450/local_maxima.sum())
mediump = max(mediump, 94)
low_worm, medium_worm, high_worm = numpy.percentile(gradient[local_maxima], [94, mediump, highp])
stringent_worm = canny.canny_hysteresis(local_maxima, gradient, low_worm, high_worm)
# Expand out 20 pixels from the stringent worm edges to make our search space
stringent_area = ndimage.binary_dilation(stringent_worm, mask=well_mask, iterations=20)
# now use the relaxed threshold but only in the stringent area
relaxed_worm = canny.canny_hysteresis(local_maxima, gradient, low_worm, medium_worm) & stringent_area
# join very close-by objects, and remove remaining small objects
candidate_worm = ndimage.binary_dilation(relaxed_worm, structure=S)
candidate_worm = ndimage.binary_erosion(candidate_worm)
candidate_worm = mask.remove_small_area_objects(candidate_worm, 30, structure=S)
# Now figure out the biggest blob of nearby edges, and call that the worm region
glommed_candidate = ndimage.binary_dilation(candidate_worm, structure=S, iterations=2)
glommed_candidate = ndimage.binary_erosion(glommed_candidate, iterations=2)
# get just outline, not any regions filled-in due to closing
glommed_candidate ^= ndimage.binary_erosion(glommed_candidate)
glommed_candidate = mask.get_largest_object(glommed_candidate, structure=S)
worm_area = ndimage.binary_dilation(glommed_candidate, mask=well_mask, structure=S, iterations=12)
worm_area = mask.fill_small_radius_holes(worm_area, max_radius=15)
candidate_edges = relaxed_worm & candidate_worm & worm_area
return candidate_edges, worm_area
def get_well_mask(image):
small_image = pyramid.pyr_down(image, 4)
smoothed, gradient, sobel = canny.prepare_canny(small_image, 2)
local_maxima = canny.canny_local_maxima(gradient, sobel)
# well outline has ~6000 px full-size = 1500 px at 4x downsampled
# So find the intensity value of the 2000th-brightest pixel, via percentile:
highp = 100 * (1-2000/local_maxima.sum())
highp = max(highp, 90)
low_edge, high_edge = numpy.percentile(gradient[local_maxima], [90, highp])
# Do canny edge-finding starting with gradient pixels as bright or brighter
# than the 2000th-brightest pixel, and spread out to the 90th percentile
# intensity:
well_edge = canny.canny_hysteresis(local_maxima, gradient, low_edge, high_edge)
# connect nearby edges and remove small unconnected bits
well_edge = ndimage.binary_closing(well_edge, structure=S)
well_edge = mask.remove_small_area_objects(well_edge, 300, structure=S)
# Get map of distances and directions to nearest edge to use for contour-fitting
distances, nearest_edge = active_contour.edge_direction(well_edge)
# initial curve is the whole image less one pixel on the outside
initial = numpy.ones(well_edge.shape, dtype=bool)
initial[:,[0,-1]] = 0
initial[[0,-1],:] = 0
# Now evolve the curve inward until it contacts the canny well edges.
gac = active_contour.GAC(initial, nearest_edge, advection_mask=(distances < 10), balloon_direction=-1)
stopper = active_contour.StoppingCondition(gac, max_iterations=200)
while stopper.should_continue():
# otherwise evolve the curve by shrinking, advecting toward edges, and smoothing
gac.balloon_force(iters=3)
gac.advect(iters=2)
gac.smooth()
gac.smooth(depth=3)
# now erode everywhere the contour edge is right on a canny edge:
gac.move_to_outside(well_edge[tuple(gac.inside_border_indices.T)])
gac.smooth()
well_mask = gac.mask
if well_mask.sum() / well_mask.size < 0.25:
# if the well mask is too small, something went very wrong
well_mask = None
return small_image, well_mask
def find_centerline_pixels(dv_coords,
mask,
sigma=1,
worm_width=50,
low_threshold=0.25,
high_threshold=0.6):
""" Find pixels along the centerline of the worm given a DV-coordinate image.
Parameters:
dv_coords: floating-point image of dorsal-ventral worm coordinates with
midline values high and edge values low. Should NOT be masked.
mask: segmented mask (approximate is ok, as ridgeline may extend out of
the masked region if the dv_coords image supports it.
sigma: gaussian blur applied to smooth the dv_coords image
worm_width: approximate width of worms at their widest at this magnification.
50 is a reasonable value for adult worms at 5x magnification.
low_threshold: lowest dv-coordinate value that could possibly be part of the
centerline.
high_threshold: lowest dv-coordinate value that would almost certainly be
part of the centerline.
Returns: all_ridges, extended_ridges, neighboring_ridges
all_ridges: all local ridglines in the image, regardless of mask. Mainly
useful for diagnostics.
extended_ridges: all low-confidence-or-better ridgelines extending from
high-confidence regions within the mask. Strictest set of ridges.
neighboring_ridges: all low-confidence-or-better ridgelines extending from
locations within three pixels of the extended_ridges. Most inclusive
set of ridges.
"""
# A horizontal ridge of dv_coords will have a positive y gradient on the low-y side of the ridge
# and a negative gradient on the other, with a zero-gradient patch right along the center of the
# ridgeline:
# y^
# |
# |-------- horizontal ridgeline of high-value dv-coordinates on a low-value background
# |
# --------->x
#
# Gradient in y direction:
# y^
# |--------
# |00000000
# |++++++++
# --------->x
#
# A vertical ridge will have a positive x gradient on the low-x side and negative on the other.
# A diagonal ridge will be a combination of the above, and the orientation of the diagonal
# can be determined by whether the low-x and low-y sides of the ridge are the same.
# I.e. if the ridge is +45 degrees, the low-x and low-y sides are opposite:
# x-gradient: y-gradient:
# y^ y^ y^
# | / ridge |++0- |--0+
# | / |+0-- |-0++
# |/ |0--- |0+++
# ------>x ------>x ------>x
# In the above the low-x side of the diagonal ridgeline is above the diagonal and the
# low-y side is below. So in this case, the x and y gradients on each side of the ridge
# are of opposite sign.
# However, if the ridge is -45 degrees, the low-x and low-y sides are both below
# the ridge, and so the gradients have the same sign.
# x-gradient: y-gradient:
# ------>x ------>x ------>x
# |\ |0--- |0---
# | \ |+0-- |+0--
# | \ ridge |++0- |++0-
# yv yv yv
#
# To find the ridgeline pixels (0 gradient surrounded by high + and - gradients on
# either side), we could look for maxima of the second derivative,
# but that is noise-prone in practice. Instead, we will take a local average of
# the absolute value of the x- and y-gradients nearby each pixel. The 0-valued ridge
# pixels will have high averages. This, however, discards the orientation information.
# To recover the degree to which the y-gradient has an + or - diagonal angle,
# we compare the local average of the product of the x and y gradients to
# the local average of the product of the absolute values of the gradients.
# This number ranges from -1 indicating that the x- and y-gradients are on
# opposite sides of the ridgeline, to +1 indicating that they're on the same sides.
# We then weight the local magnitude in the y direction by this number, to produce
# an (x, y) vector that captures the direction normal to the ridge.
#
# Given these normals, we can then locate the exact center pixels of the ridge
# by choosing pixels from the original dv_coordinate image that are local maxima
# along the ridge normal. Even if the ridgeline itself is slowly climbing or
# descending, the saddle points along the ridge will be maximal normal to the
# ridge. This technique comes from the Canny edge-finding method.
#
# Finally, we also use Canny hysteresis thresholding to extend an initial seed
# of high-confidence ridge pixels into potentially lower confidence regions:
# If a low-confidence region of ridge is connected to a high-confidence region
# (or in this implementation, within a few pixels therof), extend the ridge
# into it.
smooth_dv = ndimage.gaussian_filter(dv_coords, sigma)
ridge = smooth_dv**3
dx, dy = numpy.gradient(ridge)
adx, ady = numpy.abs(dx), numpy.abs(dy)
# average over a region about the worm's width, so choose a smoothing
# gaussian with a standard deviation about 1/4 of the width, and truncate
# at two standard deivations (1/2th of the width) on either side of the ridge
gradient_sigma = worm_width / 4
local_magnitude_x = ndimage.gaussian_filter(adx,
gradient_sigma,
truncate=2)
local_magnitude_y = ndimage.gaussian_filter(ady,
gradient_sigma,
truncate=2)
orientation = ndimage.gaussian_filter(dx * dy, gradient_sigma, truncate=2)
max_orientation = ndimage.gaussian_filter(adx * ady,
gradient_sigma,
truncate=2)
orientation /= max_orientation
all_ridges = canny.canny_local_maxima(
ridge, [local_magnitude_x, local_magnitude_y * orientation])
# Hysteresis threshold: high_mask below is regions of the local_maxima image
# that are within the overall mask region and also have a dv_coord above
# the high-confidence value. Then we extend those regions into any connected
# low-confidence regions (the low_mask regions), ignoring low-confidence
# regions not contiguous with a high-confidence region.
high_mask = mask & all_ridges & (smooth_dv >= high_threshold)
low_mask = all_ridges & (smooth_dv >= low_threshold)
extended_ridges = ndimage.binary_propagation(high_mask,
mask=low_mask,
structure=FULLY_CONNECTED)
# Now add regions of the maxima that are just a couple pixels away from the
# extended regions too.
# nearby_pixels below is regions of the low_mask that are both within the overall
# mask and near to regions in extended_ridges. Then expand out such pixels to
# all connected pixels within low_mask
nearby_pixels = mask & low_mask & ndimage.binary_dilation(
extended_ridges, iterations=3, structure=FULLY_CONNECTED)
neighboring_ridges = ndimage.binary_propagation(nearby_pixels,
mask=low_mask,
structure=FULLY_CONNECTED)
neighboring_ridges = morphology.thin(neighboring_ridges)
return all_ridges, extended_ridges, neighboring_ridges
