Fall 2022

Finite Difference Operator

The first image process I did is build 2D convolutions filter using finite difference operator:

1. Find the dx and dy in order to get the partial derivative of the image by

2. We compute the graient magnitude of the image by summing the squaring of the partial derivatives and then take the square root of it.

3. We take a threshold and make higher to 1 and lower to 0.

**Sample Outputs:**

Dx

Dy

Gradient Magnitude with Threshold of 0.25

Derivative of Gaussian (DoG)

In this part, we applied a gaussian filter on the image, then do the finite difference operator on the result blurred image.

Compare with the regular finite difference operator, the result with DoG seems to have less noise due to the blurred process, since gaussian filter is acted as a low pass filter, it will block many high frequency noises.

In addition, the edge become thick, which is also a result from blurring.

**Sample Outputs:**

Dx

Dy

Gradient Magnitude with Threshold of 0.05

Then, since the convolution is commutative, we can aternatively create the same result by first doing the difference operator on the gaussian filter, and then convolve the filters with the image. As we can see on the two result images create by double and single DoG respectively, the result are the same and can both help us to get rid of noises.

**Sample Outputs:**

Dx of Gaussian Filter

Dy of Gaussian Filter

Gradient Magnitude with Threshold of 0.05

Image Sharpening

When we have a blurry image, one technique that we can use to make the image clear is to utilizing the sharpening technique.

In order to do so:

1. We construct a low pass filter and perform it on the image to create a blurred image(low frequency).

2. Use the original image minus the blurred image to get the high frequency part of the image.

3. Finally, we add the orginal image with the high frequency part times alpha(parameter defined) to construct a sharpened image.

Taj.jpg

Sharpened

Blurred

Blurred then sharpened

Beijing.jpg

Sharpened

Blurred

Blurred then sharpened

Yasuo.jpeg

Sharpened

Blurred

Blurred then sharpened

From the result, we can see that blurred then resharp the image will not return the perfect original image. This happens because during the blurred process, it will take away some high frequency details, the sharpen process can only apply to the high frequency that remained on the blurred image, which will not include any high-frequency that lost due to the blurred process.

Hybrid Image

Next, I tried to create hybrid images by combining low frequency of one image with the high frequency of the other. Thus, if we look at the image close, we will se the high frequency image more. If we get far away from the image, we will see the low frequency image more.

Low frequency Image

High frequency Image

Hybrid Image

Low_Frequency FFT

High Frequency FFT

Hybrid FFT

**Bells & Whistles****Here are some examples with colored:**

**Potential Reason of failure: **The low frequency(basketball) has bold edges which will still remain having high frequency after doing low-pass filter and thus remains visiable in the resulting image.

Using color to enhance the effect works better on high-frequency component and it becomes clearer when watching close.

Gaussian/Laplacian Stacks

In order to create a great blending between two images, we need to first implement the Gaussian and Laplacian Stacks.

We can implemenet them by extracting the low and high frequency components of an image, then do the same on the blurred version.

Blending

Other Blending Examples

(images are properly aligned before blending)

(images are properly aligned before blending)

**Aurora at Fuji**

Fuji

Aurora

Mask

Aurora at Fuji

**Spongebob Riding Horse**

Spongebob

Horse

Mask

Spongebob Riding Horse

**Reallife Snowball**

Snowball

Pet Rabbit

Mask

Reallife Snowball

**Spongebob with Minions' Eyes**

Minions

Spongebob

Mask

Spongebob with Minions' Eyes

**Minions at Berkeley**

Minions

Berkeley

Mask

Minions at Berkeley

Reflection

In this project, I utilized filters and frequencies and applied them on various of image processing techniques including sharpening, bluring, making hybrid images and blending two images.

I enjoyed the blending process with implementation of multiresulution pyramid.

It is my first time I learned how frequency is used to create results that are blurred or sharpened.

Thank you!!