I'm working on segmentation of plant epithelial cells. My goal is to isolate cells from microCT scans and then run various metric analyses on them. Right now I am able to segment and edge detect these cells but my edge detections have gaps in them and the filled in portions are jagged. In order to fix these issues, I am converting to polar coordinates, finding the interpolation values, using linear interpolation to get smooth curves and then converting back to Cartesian Coordinates. I am running into an error where I get strange spikes in the shapes after I convert back to Cartesian Coordinates. I've attached my code and an example shape below:
##Canny Edge Detection of Edges##
#Get edge of image
#dilation = cv2.dilate(props[150].image,kernel=K,iterations = 1)
img_edges = feature.canny(props[150].image, mode='constant') #, sigma=.1)
#Sanity check
#plt.imshow(img_edges)
#Get coordinates
coords = np.argwhere(img_edges)
#Rearrange coords
coordinates = np.column_stack((coords[:,0], coords[:,1]))
sorted_coordinates = coordinates[coordinates[:, 0].argsort()]
#Finding the centroid
xX = [p[0] for p in coords]
yY = [p[1] for p in coords]
centroid = (sum(xX) / len(coords), sum(yY) / len(coords)) #xX,yY
(x_cent, y_cent) = centroid
#Plotting shape
plt.plot(coords[:,0],coords[:,1],".") #y,x
plt.scatter(sorted_coordinates[:,0],sorted_coordinates[:,1])
plt.show()
##Converting to polar coordinates##
#Defining Conversion
def cart2pol(x, y):
rho = np.sqrt(x**2 + y**2)
phi = np.arctan2(y, x)
return(rho, phi)
#Calculating distances from contours
rs, rhos = [], []
for i in range(0,len(coords),2): #5
#r, rho = cart2pol(coords[i,0]-props[150].centroid_local[0], coords[i,1]-props[150].centroid_local[1])
r, rho = cart2pol(coords[i,0]-centroid[0], coords[i,1]-centroid[1])
rhos.append(rho)
rs.append(r)
#Ensuring phi-values are in ascending order
L = sorted(zip(rhos,rs), key=operator.itemgetter(0)) #sorted(zip(rhos,rs), key=operator.itemgetter(0))
new_rho, new_r = zip(*L)
#plt.plot(new_x,new_y)
plt.scatter(new_rho, new_r, s=1) #, zorder=2)
plt.scatter(rhos, rs, s=1)
plt.title('Pre-interpolation')
plt.ylabel('r')
plt.xlabel('theta')
plt.show()
##Post-interpolation##
# Convert the new_x and new_y lists to numpy arrays
new_x = np.array(new_rho) * 1
new_y = np.array(new_r) * 1
# Sort the new_x and new_y arrays based on new_x
sorted_indices = np.argsort(new_x)
sorted_x = new_x[sorted_indices]
sorted_y = new_y[sorted_indices]
# Create evenly spaced x-values for interpolation
interpolation_range = np.linspace(sorted_x.min(), sorted_x.max(), 1000)#110)
# Perform linear interpolation
linear_interpolation = interp1d(sorted_x, sorted_y, kind='linear')(interpolation_range)
# Plot the original data
plt.scatter(new_x, new_y, label='Original Data', c='black', s = 4)
# Plot the interpolated data
plt.plot(interpolation_range, linear_interpolation, c='r', label='Linear Interpolation')
# Set labels and title for the plot
plt.xlabel('X')
plt.ylabel('Y')
plt.title('Linear Interpolation')
# Show legend
plt.legend()
# Display the plot
plt.show()
##Transforming back to Cartesian Coordinates##
def pol2cart(rho, phi):
x = rho * np.cos(phi)
y = rho * np.sin(phi)
return(x, y)
x_cart,y_cart= pol2cart(linear_interpolation,interpolation_range)
xn_cart,yn_cart= pol2cart(Xn,Yn)
plt.plot(coords[:,0],coords[:,1],".",c='red',linewidth=1)
plt.plot(x_cart+centroid[0],y_cart+centroid[1], c='blue', linewidth=2) #73,73
#plt.plot(yn_cart,xn_cart, c='blue', linewidth=2) #73,73
fig1 = plt.gcf()
aspect_ratio = 1
fig1.set_size_inches(4, 4 / aspect_ratio)
plt.show()
At first I thought this was an issue of rearranging the data points ( a version of the traveling salesman problem ), so I rearranged the x-values in ascending order but that didn't seem to fix it. Next I tried different types of interpolation and using scipy.findpeaks to removes strange peaks. Though the latter is a fix for this specific shape, it doesn't generalize very well to many different shapes. I've been stuck on this issue for 2 weeks now and would appreciate some help on this. I am fairly new to python and feel like I am missing something maybe simple?
