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Image Transformation | Digital Image Processing System

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Digital Image Processing System

In computer science, digital image processing uses algorithms to perform image processing on digital images to extract some useful information. Digital image processing has many advantages as compared to analog image processing. Wide range of algorithms can be applied to input data which can avoid problems such as noise and signal distortion during processing. As we know, images are defined in two dimensions, so DIP can be modeled in multidimensional systems.

Purpose of Image processing

The main purpose of the DIP is divided into following 5 groups:

  1. Visualization: The objects which are not visible, they are observed.
  2. Image sharpening and restoration: It is used for better image resolution.
  3. Image retrieval: An image of interest can be seen
  4. Measurement of pattern: In an image, all the objects are measured.
  5. Image Recognition: Each object in an image can be distinguished.

Following are Fundamental Steps of Digital Image Processing:

Digital Image Processing System

1. Image Acquisition

Image acquisition is the first step of the fundamental steps of DIP. In this stage, an image is given in the digital form. Generally, in this stage, pre-processing such as scaling is done.

2. Image Enhancement

Image enhancement is the simplest and most attractive area of DIP. In this stage details which are not known, or we can say that interesting features of an image is highlighted. Such as brightness, contrast, etc…

3. Image Restoration

Image restoration is the stage in which the appearance of an image is improved.

4. Color Image Processing

Color image processing is a famous area because it has increased the use of digital images on the internet. This includes color modeling, processing in a digital domain, etc….

5. Wavelets and Multi-Resolution Processing

In this stage, an image is represented in various degrees of resolution. Image is divided into smaller regions for data compression and for the pyramidal representation.

6. Compression

Compression is a technique which is used for reducing the requirement of storing an image. It is a very important stage because it is very necessary to compress data for internet use.

7. Morphological Processing

This stage deals with tools which are used for extracting the components of the image, which is useful in the representation and description of shape.

8. Segmentation

In this stage, an image is a partitioned into its objects. Segmentation is the most difficult tasks in DIP. It is a process which takes a lot of time for the successful solution of imaging problems which requires objects to identify individually.

9. Representation and Description

Representation and description follow the output of the segmentation stage. The output is a raw pixel data which has all points of the region itself. To transform the raw data, representation is the only solution. Whereas description is used for extracting information’s to differentiate one class of objects from another.

10. Object recognition

In this stage, the label is assigned to the object, which is based on descriptors.

11. Knowledge Base

Knowledge is the last stage in DIP. In this stage, important information of the image is located, which limits the searching processes. The knowledge base is very complex when the image database has a high-resolution satellite.

Image Transformation

An image is obtained in spatial coordinates (x, y) or (x, y, z). There are many advantages if the spatial domain image is transformed into another domain. In which solution of any problem can be found easily.

Following are two types of transformations:

1. Fourier Transform

Fourier transform is mainly used for image processing. In the Fourier transform, the intensity of the image is transformed into frequency variation and then to the frequency domain. It is used for slow varying intensity images such as the background of a passport size photo can be represented as low-frequency components and the edges can be represented as high-frequency components. Low-frequency components can be removed using filters of FT domain. When an image is filtered in the FT domain, it contains only the edges of the image. And if we do inverse FT domain to spatial domain then also an image contains only edges. Fourier transform is the simplest technique in which edges of the image can be fined.

Two Dimensional Fourier Transform

Image Transformation

Matrix Notation:

Image Transformation

Properties of Fourier transformation are as follows:

  • Symmetric Unitary
  • Periodic Extension
  • Sampled Fourier
  • Fast
  • Conjugate Symmetry
  • Circular Convolution


Image Transformation

Example of Blurred image and its Fourier transformation

Image Transformation

Discrete Cosine Transformation (DCT)

In Discrete Cosine Transformation, coefficients carry information about the pixels of the image. Also, much information is contained using very few coefficients, and the remaining coefficient contains minimal information. These coefficients can be removed without losing information. By doing this, the file size is reduced in the DCT domain. DCT is used for lossy compression.

One Dimension Discrete cosine transformation:

Image Transformation

Two Dimension Discrete cosine transformations:

Image Transformation

Properties of Discrete cosine transformation are as following:

  • Real and Orthogonal: C=C* → C-1=CT
  • Not! Real part of DFT
  • Fast Transform
  • Excellent Energy Compaction (Highly Correlated Data)


Image Transformation

Applications of image transforms are as follows:

  • Fourier transform is used for Edge Detection.
  • Discrete Cosine Transform is used for image compression.

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