Results

Part 1.1: Finite Difference Operator

We use the finite difference as our filter for the x and y directions:

$$ D_x = \begin{bmatrix} -1 & 1 \end{bmatrix}, \quad D_y = \begin{bmatrix} -1 \\ 1 \end{bmatrix} $$

Then we convolve the image by filters with respect to x and y, and calculate the gradient magnitude like so:

$$ G_x = Im * D_x, \quad G_y = Im * D_y, \quad G_m = \sqrt{G_x^2 + G_y^2} $$

Part 1.2: Derivative of Gaussian Filter

Given the previous approach was clearly noisy, we can apply Gaussian blur to try to reduce noise, where G is the 2D Gaussian filter. I notice that the one that has been blurred prior has darker edges and less noise, such as from the grass. The edges are also a bit rounder. A similar effect can be achieved by taking the derivative of the gaussian filters and then convolving with the difference filters to achieve the same effect with a single convolution.

Original

Binarized Gradient Magnitude

Derivative of Gaussian to Reduce Noise

Part 2.1: Sharpening

Original

alpha = 0.25

alpha = 0.5

alpha = 1

alpha = 2

alpha = 4

alpha = 0.5

alpha = 1

alpha = 2

Additionally, I tried to sharpen a blurred image. It is clear that the blurred image when sharpened is not as clear as the original, as it has a lot more noise and artifacting. This is because blurring loses information.

Original

Blurred

Blurred then Sharpened with alpha = 4

Part 2.2: Hybrid Images

Derek Low Frequency

Nutmeg High Frequency

Hybrid

Derek Original Fourier Transform

Derek Filtered Fourier Transform

Nutmeg Original Fourier Transform

Nutmeg Filtered Fourier Transform

Hybrid Fourier Transform

Sprite Low Frequency

Coke High Frequency

Hybrid

Richard Low Frequency

Lebron High Frequency

Hybrid

I think the hybrid of Lebron and I was a failure because our faces are opposites in a way. I have a lot of hair while Lebron is balding, and Lebron has a lot of facial hair whereas I have none. Thus, it is difficult to make a convincing hybrid image.

Part 2.3: Multiresolution Blending

Apple Laplacian Stack 0

Apple Laplacian Stack 1

Apple Laplacian Stack 2

Apple Laplacian Stack 3

Apple Laplacian Stack 4

Apple Laplacian Stack 5

Orange Laplacian Stack 0

Orange Laplacian Stack 1

Orange Laplacian Stack 2

Orange Laplacian Stack 3

Orange Laplacian Stack 4

Orange Laplacian Stack 5

My Merged Oraple

Laplacian Mask Level 1

Laplacian Mask Level 3

Laplacian Mask Level 5

Laplacian Mask Level 1

Laplacian Mask Level 3

Laplacian Mask Level 5

Day

Night

Blended

Laplacian Mask Level 1

Laplacian Mask Level 3

Laplacian Mask Level 5

Laplacian Mask Level 1

Laplacian Mask Level 3

Laplacian Mask Level 5

My Sister

Racket

Blended

I used a vertical binary mask similar to the oraple for the desert day and night blending, with the only difference being the dimensions which were modified to match the image. For the blend with my sister and the tennis racket, an irregular ellipse-shaped mask was used.

Bells & Whistles

For my bells & whistles, I implemented color for every aspect in at least one image. I found that for the hybrid images, color in both images worked best, and I did this for the Derek-Nutmeg hybrid. I also blended with color, and I think color is instrumental to good blending because it makes the effect that much more powerful.

Most Important Thing I Learned

In this project, I think the most important thing I learned is how operations can be combined to use only one convolution operation, which can be very useful. An example of this was the unsharp mask filter instead of subtracting a blurred image to isolate high frequencies, and then adding them.