Analysis of problems faced in Images

Overview of Image coding:

The image compression began with Context Adaptive Lossless Image Compression (CALIC) developed in 1994.

There are various Image standards which we require to know before getting into image compression namely:-

1. JPEG-LS (Joint Photographic Experts Group - Lossless)
--- Context and Mode - Single Component images :- Run mode and Regular mode.
--- Modifications for multicomponent images :- Line interleaving and Sample interleaving.
--- Prediction error correction, Quantization and Reconstruction
--- JPEG-LS entropy coding :- Regular mode coding and Run mode coding
--- JPEG-LS decoding

2. CCSDS (Consultative Committee for Space Data Systems)
--- e.Rice alogorithm
--- Adaptive Entropy Coder :- Fundamental sequence encoding, split sample option, low entropy options {Second extension and zero block option}, No compression, code selection
--- Preprocessor :- Predictor, Reference sample, Prediction error mapper.
--- Coded Data Format

3. JBIG (Joint Bilevel Image experts Group)
--- JBIG Encoding
(a) Resolution Reduction
(b)Differential layer prediction
(i) Differential typical prediction
(ii) Deterministic prediction
(iii) Bottom layer typical prediction
(iv) Model templates :- Differential layer templates and Bottom layer templates
(v) Adaptive arithmetic coding
--- Data structure and formatting
--- JBIG decoding
The improved form of JBIG2 decoding was introduced, which is divided into text, halftone and generic regions. It allows the formation of arbitrary symbol dictionaries.
JBIG2 decoding procedures:-
--- Generic region decoding
--- Generic refinement region decoding
--- Symbol dictionary decoding
--- Text region decoding
--- Pattern dictionary decoding
--- Halftone region decoding

4. JPEG2000
Features:- Compressed domain image processing/editing and Progression.
JPEG2000 algorithm:
--- Tiles and component transforms
--- Wavelet transform
--- Quantization
--- Bit-plane coding
--- Packets and layers
--- CodeStream

5. PNG (Portable Network Graphics)

PNG is a progressive format that was originally designed to replace GIF. The PNG format has a set of new features that GIF lacks. PNG is also performed under a lossless compression that follows Deflate algorithm.

6. TIFF (Tagged Image File Format)

The TIFF was released in 1986 and It was used to hold scanned white and black images. It uses JPEG compression algorithm. It is a rich and flexible file format, supported by many programs.

7. BMP (Microsoft Windows BitMap)

Bitmap is a Windows raster format, which is used for all possible raster data storage. It works under RLE compression algorithm. The current format version is device independable and makes possible to record images of a different quality level.

8. GIF (Graphics Interchange Format)

GIF is used to hold and transfer images in index color mode (not more than 256). The format also supports a lossless LZW compression algorithm and interlaced mode (interfaced image load). It supports an additional channel to perform a transparency effect and to hold a set of images in a single file, where frame show time and animation were displayed. Nowadays, the format is one of the most popular graphic formats. Yet, it not suited to hold a photorealistic images, since it doesn't contain more than 256 colors. It is mostly used to display animation and drawing pictures without blend.

9. WMP (Microsoft Windows MetaFile)

WMF files has the capability to hold vector and halftone images in working memory or in disks with post output display. The Windows Metafile format is a specific Windows format, which is supported by a lot of non — Windows applications for data exchange with Windows applications. WMF format is considered to be a general format for graphic applications and is supported by all platforms.

10. PCX (PC Paint Brush file format)

PCX format is one of the most usable graphic formats. It was designed by Zsoft for PC Paintbrush MS-DOS, which is the reason that it is also known as PC Paintbrush format. PCX files are used for graphic data storage and exchange in desktop publishing system. Unfortunately, its compression algorithm is not effective enough to hold images with large pixel intensity, though the image data is encoded with the help of one of the RLE algorithm.

Understanding Image Coding:-

Starting with the image characterization mathematically :--- It’s divided into two types namely ‘deterministic image representation’ and ‘statistical image representation’. The deterministic image representation is termed as the definition of mathematical image functions that are being used including the image point properties. The statistical image representation is termed as the image specification by a set of properties.

The image is generally represented by two spatial co-ordinates with wavelength and time. Coming to two-dimensional image systems, we will across some operators namely ‘Singularity operators’, ‘ additive linear operators’ and ‘differential operators’.

The singularity operators are termed as the analysis of the two dimensional systems. Example:- Dirac delta function.

The additive linear operators which comes under additive linear system is one of the two-dimensional system that obeys and follows the law of additive superposition. The additive superposition can also be extended to general mapping. The input function of two spatial co-ordinates is represented as the sum of amplitude weighted Dirac delta function by means of string integral. The impulse response mechanism is used where the linear operators will be applied only to the dependent integrand. The impulse response preferably known as point spread function when the mechanism is applied in optical systems. When the impulse response has the ability to extend the additive superposition integral, then it leads to the additive linear two-dimensional system known as space invariant. In a space invariant system, the superposition integral reduces through convolution integral. The visualizations are provided in convolution process through input functions along with impulse response.

The differential operators comes under the spatial differentiation of image field where it is used for edge detection in images enhancing the performance through the threshold operation for finding points of amplitude change. The spatial derivatives are done both horizontally and vertically, where it flows in a vector direction through horizontal axis and the sum of these two derivatives are known as Laplacian operator.

Coming to the two-dimensional Fourier transform, it is computed in terms of ‘separability’, ‘linearity’, ‘scaling’, ‘shift’, ‘convolution’, ‘Parseval’s theorem’, ‘Autocorrelation theorem’ and ‘spatial differentials’.

Now comes the “representation of color spaces”…
1. Non-Standard <------> Colorimetric linear RGB == Linear and Non-linear inter-component transformation
2. Colorimetric linear<------> Colorimetric linear RGB == Linear inter-component transformation
3. Colorimetric non-linear<------> Colorimetric linear RGB == Non-Linear inter-component transformation
4. Video gamma RGB <------> Colorimetric linear RGB == Non-linear point transformation
5. Video gamma RGB <------> Video gamma lumia/chroma YCC == Linear inter-component transformation
6. Colorimetric linear RGB<------> Subtractive CMY/CMYK == Linear point transformation, Non-linear inter-component transformation

Image sampling can be done in a grid spaced array of Dirac delta function through the spatial coordinates. The fourier transform methodology is used, where it uses convolution theorem for determining sampled image spectrum by changing the order of summation through integration and invoking the property of Dirac delta function.

The image reconstruction systems can be done through:-
1. Cathode Ray Tube --- This is physics oriented, so let’s skip it for now.
2. Reconstruction filters

How image reconstruction is done through image sampling?
After obtaining the image samples, the continuous image field can be obtained through linear spatial interpolation or filtering where the transfer function is represented by the continuous domain impulse response by interpolation filter. Through convolution of samples, the reconstructed image is being obtained with reconstruction filter impulse response.

The Nyquist criterion is followed which helps to check whether the image is ‘over-sampled or under-sampled’. If the image is sampled preventing the overflow, then the approximate reconstructed image will be obtained.

The image sampling mostly follows ‘rectangular reconstruction filter’ and ‘circular reconstruction filter’. The image is reconstructed with these filter through an infinite sum of Sin(theta) functions known as sinc functions. Also, an alternative reconstruction filter named ‘cylindrical filter’, which can be implemented with the help of a transform function. The impulse response uses the first-order Bessel function when there are more reconstruction filters or interpolation waveform, where it helps in building a perfect reconstructed image.

The spectrum of sampled noise indicates that if the noise process is under-sampled, then it’s tails will overlap into the pass-band of the reconstructed image filter leading to additional issues. The only solution to this issue is to pre-filter the noisy image before sampling, which will thereby help in reducing the noise bandwidth.

Analyzing the faced during Image Coding:

In text compression, there were supporting existing mechanism that follows lossless compression. Other than text, the image coding follows lossy compression for images where the colours and pixels are affected. Also, there are issues seen in image rendering and unicodes.