Project 2 - Fun with Filters and Frequencies!¶

By Yiwen Chen¶

1.1¶

The partial x and y derivatives are computed by convolving the cameraman image with D_x and D_y respectively.The gradient magnitude is computed by taking the square root of the sum of the partial derivatives squared.Results of partial x and y derivatives and gradient magnitude are shown below (with threshold set to 0.001). However in order to show important edges of the man and the camera, noises in the lake are also reserved.

1.2¶

Below is the result of applying gaussian filter before taking derivatives. Compared with result without gaussian filter, we can see the noise in the lake is eliminated and we can choose a lower threshold so that edges of cameraman are more clear.

Below are x derivative of gaussian filter, y derivative of gaussian filter and the resulting image. The resulting image is the same as applying gaussian before taking derivatives.

1.3¶

The rotating angle is chosen by picking the angle that results in highest vetical plus horizontal frequency in the orientation histogram.

Before rotation

After rotating 4 degree

The original image of Pisa Tower

After rotation

Before rotation

After rotation

Failure case: the straigthening process fails because of the stripes on the phone case

After rotation

2.1¶

We can collect hight frequent part of a image by subtracting the low frequent part from it. By adding these high frequencies to the original image, we can get a sharpened version of the original image. The whole process can be combined into a single convolution operation called the unsharp mask filter

Below is the original taj and sharpend maj.