Week 4 – Progress report

During this week I have studied image transformations: a way to represent images in different spaces. Image trasformation is used for filtering/scaling/rotating source images, for recognizing patterns/primitives, for reducing space dimension.

It follows a list of the image transformation algorithms that I have treated with a short description (and a sample image – the source image is the same from previous post ). I have decided to split the list into 2 parts: the first presenting convolution algorithms, the last presenting more complicated image transformation.

CONVOLUTION

Sobel: Sobel kernels are used to compute the derivates of an image. For each pixel is calculate the derivate along the x and y direction: this can be used to identify gradient of the image.

Sobel derivaties along x and y directions.

Laplace: a Laplace operator is a double derivate (). Zeros of the Laplacian operator corresponds to edges (abrupt changes in intensity) in the source image.

It highlights the key contour.

Canny: Canny edge detector uses a blurred image (using Gaussian filter) and apply a hysteresis filter (it has 2 thresholds). In order to recognize a pixel as non edge its intensity must be lower than T_l; to be an edge its intensity must be higher than T_h.

It extracts the key edges.

COMPLEX TRANSFORMATION

Hough: represents every pixels with the distance from the origin and the rotation with respect to the reference axis . It is used to recognized lines and circles features in images.

On the left Hough identifies main line components in the image, on the right it identifies circles (wrongly because the image does not contain many circular primitives)

LogPolar: represent the image in Polar coordinates (instead of rho is used its logarithmic value). It has been inspired by human vision: a LogPolar image represent the source image as it were seen by a human eye (more attention and details close to the center).

On the left the LogPolar transform, on the right the inverse transformation (it helps to understand what we represent in the LogPolar space)

DFT: it stands for Discrete Fourier Transform. It represent the image as a sum os sin and cos function. It is used for filtering: since convolution in Fourier space is a simple multiplication, it is possible to apply bigger kernel with smaller computational effort.

On the left the magnitude of the real and imaginary part after the Fourier transform, on the right the inverse transformation.

Next steps:
1. Apply PCA to a filtered image
2. Approach Neural Network algorithms