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Labs/Lab_3_LiDAR_ML_Segmentation/getEigenvaluePCA.py

+def getEigenvaluePCA(a, b, c, dim, decim=2):
+	"""
+	Function to estimate the eigenvalues of the PCA 
+	for every points into a given sphere of radius dim/2
+	------
+	INPUT:
+		@a, @b, @c: numpy arrays with the coordinates
+		@dim	  : float - diameter of interest of the neighborhood ball
+		@decim	: integer - decimation factor to lower the time processing.
+	-----
+	OUTPUT:
+		@comp	 : array of array with the 3 eigenvalues
+	
+	EXAMPLE: 
+		[[0.68693784 0.31106007 0.0020021 ]
+		 [0.75319626 0.24592732 0.00087642]
+		 [0.78309201 0.21595601 0.00095197]
+		 ...]
+	
+	"""
+	from sklearn.decomposition import PCA
+	from scipy import spatial
+	
+	
+	
+	print('Data are decimed by a factor of ', decim)
+	# Remove the mean of each vector
+	a -= np.mean(a, axis=0)
+	b -= np.mean(b, axis=0)
+	c -= np.mean(c, axis=0)	
+	# Concat the coordinates arrays into a single matrix.
+	Y = np.c_[a[::decim], b[::decim], c[::decim]]
+	print("shape of Y " ,np.shape(Y))
+
+	# Estimate the distance of one point with every neighbour around
+	dist = spatial.distance.squareform(spatial.distance.pdist(Y))	
+	
+
+	
+	n_samples = Y.shape[0]		   # number of points in Y
+	
+	print('  Treating distance of', dim, 'm')
+	comp = []						# Initialize the eigenvalues components array
+
+	# Loop over every points to have a look on its neighbour.
+	#   1. We consider a sphere of radius dim/2 and we only consider 
+	#				the neighbours inside this sphere
+	#   2. We create a subsample with these points
+	#   3. Using PCA scikit-learn function, we estimate the 3 eigenvalues of these points
+	#   4. We concatenate these 3 eigenvalues in a single array which will be return at the end.
+	for kk in range(0,n_samples):
+		pts = np.where((dist[kk,:]<=dim/2))  # Mask of values corresp. to the criteria
+											 
+
+		if np.size(pts)<3:			 # Check if the number of neighbour is sufficient	 
+			print("Revise dims: ")
+			print(pts)
+			print(dist)
+		else:
+			Ytmp = Y[pts,:]			 # Apply the criteria on the dataset
+			Ytmp = Ytmp[0,:,:]		  # Reduce the depth of the array	   
+										# (not necessary depending on the data structure used)
+										# Equivalent to Ytmp = np.squeeze(Ytmp)
+
+			pca = PCA(n_components=3)   # Instantiate the PCA object 
+			pca.fit(Ytmp)
+			eigenvalues = pca.explained_variance_ratio_
+			#sval = pca.singular_values_
+			#print('------')
+			#print( eigenvalues) 
+			#print( sval**2 / np.sum(sval**2) )
+			comp.append(eigenvalues)	# Append the 3 eigenvalues to "comp" array
+	comp = np.array(comp)
+	return comp
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