1.1: Finite Difference Operator
Original
Convolution with Finite Difference in the x direction
Convolution with Finite Difference in the y direction
Gradient Magnitude Image
Binarized Edge Image (treshold = 0.3)
1.2: Derivative of Gaussian Filter
Convolution with Gaussian Kernel (Blurred Image)
Convolution of Blurred Image with D_x
Convolution of Blurred Image with D_y
Blurred Gradient Magnitude
Binarized Edge Image (treshold = 0.07)
Note above that the edge image on the blurred image is much less noisy than before.
Additionally, the edges are typically thicker and have fewer discontinuities than when using the difference filter on the original iamge.
Original Gaussian Filter
Gaussian Convolved with D_x
Gaussian Convolved with D_y
Blurred Gradient Magnitute from DoG
Binarized Edge Image (treshold = 0.07)
Here the results of convolving twice (first with the Gaussian and then the D_x/D_y) filters are the same as the results of convolving with the combined filter.
2.1: Image "Sharpening"
Taj Mahal
Original
Blurred
Sharpened
Blurred
Sharpened
Bird
Original
Blurred
Sharpened
Blurred
Sharpened
Boats
Original
Blurred
Sharpened
Blurred
Sharpened
Blurring and unblurring a sharp image
Discussion: The unsharp mask filter made the image appear sharper overall. The dark lines on the orginal images were emphasized, which makes the image more visually striking. But sharpening the blurred image does not recover the original image perfectly, possibly due to the loss of high frequencies during the blurring process.
2.2: Hybrid Images
Derek/Nutmeg
Tiger/Dog
28 Boy/Owl
Log magnitudes of FFTs of an image of a boy
Low pass filtered version
Log magnitudes of FFTs of an image of an owl
High pass filtered version
Sum of the above low pass filtered and high pass filtered version
Hybrid Image
Discussion:
The boy and Owl image is my favorite. The two subjects here share similar facial structures, which makes
alignment easy. Also, the owl has complex feather structures, which is well perserved in
high frequency.
Failure
Discussion:
This is an example of failure. The subjects of the two images here don't align, which means that when you tries to decipher
the low frequency image, the high frequency one will distract you negatively.
Discussion: The boy and Owl image is my favorite. The two subjects here share similar facial structures, which makes alignment easy. Also, the owl has complex feather structures, which is well perserved in high frequency.
2.3: Gaussian and Laplacian Stacks
Apple Half
Orange Half
Combined!
Final result
Output Image