improc ass4: Added samples, Gaussian filter and timer.

improc/ass4/gauss.py

+#!/usr/bin/env python
+from numpy import zeros, arange, pi, e, ceil, meshgrid
+from matplotlib.pyplot import imread, imshow, plot, xlabel, ylabel, show, \
+        subplot, xlim, savefig
+from mpl_toolkits.mplot3d import Axes3D
+from scipy.ndimage import convolve
+from time import time
+from sys import argv, exit
+
+def Gauss(s):
+    """Create a sampled Gaussian function of scale s."""
+    size = int(ceil(3 * s))
+    W = zeros((2 * size + 1, 2 * size + 1))
+    t = s ** 2
+    a = 1 / (2 * pi * t)
+
+    # Sample the Gaussian function
+    for x in xrange(-size, size + 1):
+        for y in xrange(-size, size + 1):
+            W[x, y] = a * e ** -((x ** 2 + y ** 2) / (2 * t))
+
+    # Make sure that the sum of all kernel values is equal to one
+    return W / W.sum()
+
+def plot_diff(F, s):
+    """Calculate and plot the convolution of scale s of an image F."""
+    W = Gauss(s)
+    G = convolve(F, W, mode='nearest')
+
+    # Original image
+    subplot(131)
+    imshow(F, cmap='gray')
+
+    # Gauss function
+    x = arange(W.shape[0])
+    X, Y = meshgrid(x, x)
+    ax = subplot(132, projection='3d')
+    ax.plot_surface(X, Y, W, rstride=1, cstride=1, cmap='jet')
+    ax.set_zlim3d(0, 1)
+    ax.set_xlabel('x')
+    ax.set_ylabel('y')
+    ax.set_zlabel('g(x, y)')
+
+    # Convolution
+    subplot(133)
+    imshow(G, cmap='gray')
+
+    show()
+
+def exit_usage():
+    print 'Usage: python %s timer [ FILE ] | diff [ SCALE ]' % argv[0]
+    exit(1)
+
+if len(argv) < 1:
+    exit_with_usage()
+
+F = imread('cameraman.png')
+
+if argv[1] == 'timer':
+    # Time for multiple scales
+    S = [1, 2, 3, 5, 7, 9, 11, 15, 19]
+    repeat = 1
+    timings = []
+
+    for i, s in enumerate(S):
+        t = 0
+
+        for k in xrange(repeat):
+            W = Gauss(s)
+            start = time()
+            convolve(F, W, mode='nearest')
+            t += time() - start
+
+        timings.append(t / repeat)
+
+    xlim(S[0], S[-1])
+    xlabel('s')
+    ylabel('time (s)')
+    plot(S, timings, 'o-')
+
+    if len(argv) > 2:
+        savefig(argv[2])
+
+    show()
+elif argv[1] == 'diff':
+    if len(argv) < 2:
+        exit_with_usage()
+
+    plot_diff(F, int(argv[2]))

improc/ass4/samples.py

+#!/usr/bin/env python
+from numpy import arange, meshgrid, pi, sin, cos
+from matplotlib.pyplot import subplot, imshow, show, quiver
+
+# Create sample axes
+x = arange(-100, 101)
+y = arange(-100, 101)
+xx = arange(-100, 101, 10)
+yy = arange(-100, 101, 10)
+
+Y, X = meshgrid(x, y)
+YY, XX = meshgrid(yy, xx)
+
+# Configure constants
+A = 1
+B = 2
+V = 6 * pi / 201
+W = 4 * pi / 201
+
+# Create sample data
+F = A * sin(V * X) + B * cos(W * Y)
+Fx = A * V * cos(V * X)
+Fy = -B * W * sin(W * Y)
+FFx = -A * V ** 2 * sin(V * XX)
+FFy = -B * W ** 2 * cos(W * YY)
+
+# Plot F, Fx and Fy sample data next to each other
+# Show FFx and FFy as a quiver plot over F
+subplot(131)
+imshow(F, cmap='gray', extent=(-100, 100) * 2)
+quiver(yy, xx, FFy, -FFx, color='red')
+subplot(132)
+imshow(Fx, cmap='gray')
+subplot(133)
+imshow(Fy, cmap='gray')
+show()