Dela

assignment3/solution.py

@@ -153,8 +153,9 @@ def one_d() -> None:
 ############################################
 
 def ex2():
-    two_a()
+    #two_a()
     two_b()
+    two_c()
 
 
 def two_a():
@@ -190,14 +191,66 @@ def two_b():
     derivative magnitude). You only need to compute the comparison to actual pixels,
     interpolating to more accuracy is not required.
     """
-    SIGMA = 0.5
-    THETA = 0.16
+    SIGMA = 1
+    THETA = 0.01
 
     museum = uz_image.imread_gray('./images/museum.jpg', uz_image.ImageType.float64)
     museum_edges = uz_image.find_edges_nms(museum, SIGMA, THETA)
     plt.imshow(museum_edges, cmap='gray')
     plt.show()
 
+def two_c():
+    """
+    The final step of Canny’s algorithm is edge tracking by hysteresis.
+    Add the final step after performing non-maxima suppression along edges. Hysteresis
+    uses two thresholds tlow < thigh, keeps all pixels above thigh and discards all pixels
+    below tlow. The pixels between the thresholds are kept only if they are connected to
+    a pixel above thigh.
+    Hint: Since we are looking for connected components containing at least one pixel
+    above thigh, you could use something like cv2.connectedComponentsWithStats to
+    extract them. Try to avoid explicit for loops as much as possible
+    """
+    SIGMA = 1
+    THETA = 0.02
+    T_LOW = 0.04
+    T_HIGH = 0.16
+
+    museum = uz_image.imread_gray('./images/museum.jpg', uz_image.ImageType.float64)
+
+    connected = uz_image.find_edges_canny(museum, SIGMA, THETA, T_LOW, T_HIGH)
+
+    plt.imshow(connected, cmap='gray')
+    plt.show()
+
+############################################
+# EXCERCISE 2: Exercise 1: Edges in images #
+############################################
+def ex3():
+    three_a()
+    #three_b()
+    #three_c()
+
+def three_a(): 
+    """
+    Create an accumulator array defined by the resolution on ρ and ϑ values. Calculate the 
+    sinusoid that represents all the lines that pass through some nonzero point.
+    Increment the corresponding cells in the accumulator array. Experiment with different 
+    positions of the nonzero point to see how the sinusoid changes. You can set
+    the number of accumulator bins on each axis to 300 to begin with.
+    """
+
+    x_y_values = np.array([[10, 10], [30, 60], [50, 20], [80, 90]])
+
+    fig, axs = plt.subplots(2, 2)
+    fig.suptitle('Trasformation of points into hugh space')
+
+    for i in range(0, 4):
+        accumulator = uz_image.hough_transform_a_point(x_y_values[i][0], x_y_values[i][1], 300)
+        axs[i // 2, i % 2].imshow(accumulator)
+        axs[i // 2, i % 2].set_title(f'x = {x_y_values[i][0]}, y = {x_y_values[i][1]}')
+
+    plt.show()
+
 
 
 # ######## #
@@ -206,7 +259,7 @@ def two_b():
 
 def main():
     #ex1()
-    ex2()
+    #ex2()
     #ex3()
 
 if __name__ == '__main__':

assignment3/uz_framework/image.py

@@ -611,3 +611,46 @@ def find_edges_nms(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]],
                 reduced_magnitude[y, x] = 0
  
     return reduced_magnitude
+
+
+def find_edges_canny(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], sigma: float, theta: float, t_low: float, t_high: float) -> Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]:
+    """
+    Aceppts: image, sigma, theta, t_low, t_high
+    Returns: image with edges
+    """
+
+    image_nms = find_edges_nms(image, sigma, theta)
+    image_nms[image_nms < t_low] = 0
+    image_nms[image_nms >= t_low] = 1
+
+    image_nms = image_nms.astype(np.uint8)
+    new_image = np.zeros_like(image_nms)
+    
+    num_labels, labels, _, _ = cv2.connectedComponentsWithStats(image_nms, connectivity=4, ltype=cv2.CV_32S)
+    
+    for i in range (1, num_labels):
+        idxs = np.where(image_nms[labels == i] > t_high)
+
+        if idxs != []:
+           new_image[labels == i] = 1
+
+    return new_image
+
+
+def hough_transform_a_point(x: int, y: int, n_bins: int) -> npt.NDArray[np.float64]:
+    """
+    Accepts: x, y, n_bins
+    Returns: x, y transformed into hough space
+    """
+    theta_values = np.linspace(-np.pi/2, np.pi, n_bins)
+    
+    cos_theta = np.cos(theta_values)
+    sin_theta = np.sin(theta_values)
+    accumlator = np.zeros((n_bins, n_bins))
+
+    for i in range(n_bins):
+        r = np.round(x * cos_theta[i] + y * sin_theta[i]) + n_bins/2
+        accumlator[int(r), i] += 1
+
+    return accumlator
+