The document discusses JPEG standards and methodology. The key points are: - JPEG defines baseline, extended, and special lossless systems. Baseline must reasonably decompress color images with 4-16 bits/pixel and high compression. - Compression uses discrete cosine transform (DCT) to transform spatial domain to frequency domain, quantization to optimize for human eye, and entropy encoding like Huffman coding to minimize file size. - DCT represents signals with fewer points in frequency domain than spatial domain. Quantization further reduces precision for more compression. Entropy encoding assigns codes to coefficients based on probability.

1. Standard
and
Methodology
JPEG

2. JPEG Standards
• Baseline system
• Extended system
• Special lossless system

3. JPEG Standards
• Every codec must implement this.
Base line system must reasonably decompress colour image
maintain, a high compression ratio, and handle from 4 bit/pixel to
16 bits/pixel.
• Extended system covers the various encoding aspects such as
variable length encoding, progressive encoding and the
hierarchical mode of encoding.
• The special lossless function ensures that at resolution at which
the image is compressed, decompressed results in no loss of any
details that was there in the original source image.

4. JPEG Components
• Baseline Sequential Codec:
– Consists of 3 steps:
• Formation of DCT coefficient
• Quantisation
• Entropy
• DCT Progressive Mode:
– The key steps of formation of DCT coefficient and quantization are the same as for the
baseline sequential codec. The key difference is that each image component is coded
in multiple scans instead of single scan.
• Predictive Lossless Encoding:
– A predictor combines sample area and predict neighbouring area on the basis of
sample area. The predicted area are checked against the fully lossless sample for each
area and difference is encoded.
• Hierarchical Mode:
– It provides a means of carrying multiple resolution. Each successive encoding of the
image is reduced by the factor of two, in either the horizontal or vertical dimension.

5. JPEG Methodology
• JPEG Compression is lossy.
• Compression uses
• DCT (Discrete Cosine Transform)
• Quantisation
• Entropy
• DCT: removes redundancy by transforming data from spatial domain to
a frequency domain.
• Quantizer: Quantises the DCT coefficient with weighting function to
generate quantized DCT coefficient optimized for human eye.
• Entropy: Minimizes the entropy of the quantized DCT coefficient.

7. DCT (Discrete Cosine Transform)
• In time domain the signal requires lots of data points to
represents the time in x-axis and amplitude in y-axis. Once the
signal is converted in to a frequency domain, only few points
are required to represent the same signal.
• The technique can be applied to a colour image. To compress a
gray scale image in JPEG, each pixel is translated into luminance
or gray values.
• To compress an RGB colour image, the work is three times as
much, because JPEG treats each colour component separately.
• Red compressed first, then Green lastly Blue.

9. DCT (Discrete Cosine Transform)
• Benefits
– Proven to be optimal transform for large classes of image.
– DCT is orthogonal transform.
• Spatial->frequency (where only few points required)
– DCT generates coefficient that are easily quantized to achieve good
compression of block.
– DCT algorithms are well behaved and can be computed efficiently.
– DCT algorithms are symmetrical
• So inverse is also possible.

10. DCT Calculation
• C(i)C(j)= Normalization Factors.
• Pixel(x,y)=2D image.
• Cos factor and summation is added two times because one for row and
another one for column.

11. DCT Calculation
• The output matrix represents the frequency domain DCT components.
Row 0 column 0 has the coefficient 0f 172. This coefficient is much
larger than other 63. so it is called as DC coefficient and other are
called AC coefficient.

12. Quantization
• Quantization is process of reducing the precession of an integer
there by reducing the number of bits required to store the inte
ger.
• DCT matrix is quantized to increase the compression.
Quantized Coefficient (i,j)=DCT(i,j)/Quantum(i,j)
• As the quantum value gets larger the quantisation coefficient
gets smaller.
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13. 13

14. Zigzag Sequence
• The zigzag sequence starts at DC coefficient value.
• Zigzag ordering is designed to facilitate entropy coding .

15. Entropy Encoding
• Uncertainty in a substance.
• When the energy possessed to do the work decreases the
entropy increases.
• In Information theory a system that has a high degree of
unpredictability has high entropy.
• In data compression it is measure of the information content of
a message in number of bits.
• Entropy in number of bits=log 2(probability of object)

16. Entropy Encoding
• Example: Represent ‘T’
• Probability of T’s presence in a text string =
1/8
• Number of bits of entropy=3 bits.
• If 7 T’s in text then=21 bits
• In ASCII 8bit=56 bits

17. Entropy Encoding
• 2 types
– Huffman coding
– Arithmetic coding
• Huffman coding requires that one or more coding
sets of code table be specified by the application for
coding and decoding. Table may be predefined or
computed specifically for a given image.
• Arithmetic coding does not require tables. It is able
to adapt to the image statistic as it encode the
image

18. DC Coefficient Coding
• DC components are differentially coded as
(SIZE, Value)
– Size: Encoded with a variable length code from
Huffman table
– Value: Encoded with a variable length integer.
– D=DCx-DCx-1
• The code for a Value is derived from the
following table

19. Example: If a DC component is 40 and the previous DC component is 48.
The difference is -8. Therefore it is coded as: 1010111
0111: The value for representing -8
101: The size from the same table reads 4. The corresponding code from
the table at left is 101.
19

20. AC Coefficient Coding
• AC components are differentially coded as
(Run length, size)
• Run length: Number of consecutive zero-valued AC
coefficient in the zigzag sequence matrix preceding a
non zero AC coefficient.
• Size: Number of bits used to encode the amplitude
of the AC coefficient.