Digital Image Processing

Aim

After completing the course:

• The student should be able to explain the basic theory for 1D and 2D continuous Fourier transform with associated theorems, sampling, reconstruction, and DFT. The student should be able to explain the basic theory of digital images (two-dimensional signals), for example, 2D discrete convolution, resampling, interpolation, and scale space. The student should be able to explain simple convolution kernels and filters for derivation, low-pass, and high-pass filtering. The student should be able to perform related calculations.
• The student should be able to explain several of the classic image analysis methods, see the course content. The student should be able to explain color models and color transformations for images. The student should be able to perform related calculations.
• The student should be able to perform calculations on images, using a high-level language such as Python and/or Matlab. This includes interpreting the results 2D Fourier transforms, as well as solving simple image analysis problems.

Content

The course consists of 2 parts. The first part intends to provide basic knowledge of signal processing on images. This knowledge provides a good foundation for the second part, which is devoted to classical image analysis methods, and color.

1) Basic signal processing on images:

• The digital image. Color tables.
• Repetition of the 1D Fourier transform. From 1D to 2D Fourier transform. Theorems for 1D and 2D Fourier transform, such as scaling, translation, derivative, convolution, and multiplication. Theorems for 2D Fourier transform such as the rotation theorem. Look at images and their Fourier transforms and relate these to the theorem.
• The Dirac pulse. Sampling and reconstruction. Effects on the image in the case of aliasing in the spatial or Fourier domain.
• 1D and 2D DFT. Discrete 1D and 2D convolution. Convolution kernels in spatial and Fourier domain: low pass (Gaussian), high pass (Laplace), derivative (Sobel).
• 2D geometric operations. Resampling and interpolation. Scale space.

The computer exercises:

1) Operations on gray scale images. Linear filters in the spatial and Fourier domain.

2) Resampling and interpolation.

2) Classical image analysis methods, and color.

• Segmentation: Regional growing, watersheds, labeling.
• Operations on histogram. Thresholding: automatic, local, and with hysteresis.
• Binary image processing: Morphological operations, distance transform, connectivity preserving operations, feature extraction, chain code, polygon approximation, and Fourier descriptors.
• Matched filters and pattern recognition. Edge detection with Sobel and Canny. Hough transform. Line detection. Corner detection. The structure tensor.
• Image restoration: Inverse filtering, wiener filtering.
• Non-linear filters: Homomorphic filtering, median filter, max- and min-filter, etc.
• Color models. Color transformations. Color segmentation.

The computer exercises:

3) Operations on binary images. Histogram and color tables.

4) Automatic thresholding and simple OCR (Optical Character Recognition).

5) Segmentation of cells in microscopy images.

6) Automatic counting of blood cells.

7) Image restoration. Edge detection with Hough transform and Canny. Non-linear filters.