cs148: introduction to computer graphics and imaging...
TRANSCRIPT
![Page 1: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/1.jpg)
CS148: Introduction to Computer Graphics and Imaging
Compression
![Page 2: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/2.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Key Concepts
Lossless vs. lossy compressionKolmolgorev complexityPredictive coding / Huffman codingJPEG / Discrete cosine transform (DCT)JPEG2000 / Wavelets
![Page 3: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/3.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Image and Video Data Rates
Image 640x480x24b = ~3/4 MB
Full screen Image 1024x768x24b = ~2.5MB
DVD 720x480x24bx30f/s = ~30 MB/s
High Definition DVD 1920x1080x24bx30f/s = ~178MB/s
Film 4000x3000x36bx30f/s = ~1.5GB/s 8 TB for one 90 minute movie!
![Page 4: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/4.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Lossless vs. Lossy Compression
Lossless All information stored Exact original can be reconstructed
Lossy Some information discarded Goal: discard information humans won’t
notice Much higher compression ratios possible
![Page 5: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/5.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Kolmogorov Complexity
What is the shortest program that can generate the data?
17 KB JPEG
Re(c), Im(c), xmin, xmax, ymin, ymax (24B)
z0 = x + iy
zn+1 = z2n + c
![Page 6: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/6.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Run Length Encoding
BWBBBBBBBBBBBBWWWWWWBBBW
BW\{12}B\{6}W\{3}BW
![Page 7: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/7.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Code Book
Alphabet: A, B, C, DFrequencies: ¼, ¼, ¼, ¼ Code: 00, 01, 10, 11
ABCDBDAC = 8 characters00 01 10 11 01 11 00 11 = 16 bits
¼ * 2 + ¼ * 2 + ¼ * 2 + ¼ * 2 = 2 bits/ch on average
![Page 8: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/8.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Code Book
Alphabet: A, B, C, DFrequencies: ½, ¼, 1/8, 1/8Code: 0, 10, 110, 111
ABACADAB = 8 characters0 10 0 110 0 111 0 10 = 14 bits
½ * 1 + ¼ * 2 +1/8 * 3 +1/8 * 3 = 1 ¾ bits/ch on average
![Page 9: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/9.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Entropy
![Page 10: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/10.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Huffman CodingA
(.10)
B (.15)
C(.30)
D(.16)
E(.29)
![Page 11: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/11.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Huffman Coding
A (.10)
B (.15)
C(.30)
D(.16)
E(.29)
AB (.25)
0 1
![Page 12: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/12.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Huffman Coding
A (.10)
B (.15)
C(.30)
D(.16)
E(.29)
AB (.25)
0 1
ABD(.41)
0 1
![Page 13: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/13.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Huffman Coding
A (.10)
B (.15)
C(.30)
D(.16)
E(.29)
AB (.25)
0 1
ABD(.41)
0 1 0 1
CE(.59)
![Page 14: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/14.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Huffman Coding
A (.10)
B (.15)
C(.30)
D(.16)
E(.29)
AB (.25)
0 1
ABD(.41)
0 1 0 1
CE(.59)
0 1
ABCDE(1.0)
![Page 15: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/15.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Lossy Compression
Chroma subsamplingTransform Coding
Fourier / DCT (JPEG) Wavelets (JPEG2000)
![Page 16: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/16.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Chroma Subsampling
+
![Page 17: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/17.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Transform Coding
X = 2 2 2 2 3 4 5 6 6 6 6 H(X) = 2.0049
D(X) = 2 0 0 0 1 1 1 1 0 0 0 H(D(X)) = 1.3222
Difference Operator
![Page 18: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/18.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Bases
Basis vectors b0, b1, … , bn
Express any vector as
a0 * b0 + a1 * b1 + … + an * bn
where the coefficients ai are scalars.
![Page 19: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/19.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Pixel Basis
![Page 20: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/20.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Another Basis
![Page 21: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/21.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Two Observations on Images
Characterize images by the frequencies that are present
The frequencies in natural images fall off as 1/f That is, high frequencies are less common
The human visual system is less sensitive to high frequencies
That is, it is more important to preserve low frequencies than high frequencies
![Page 22: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/22.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Discrete Cosine Transform (DCT)
![Page 23: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/23.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
DCT
![Page 24: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/24.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
DCT
262,144 pixels 43384 largest terms, 16%(dropped 218,760 terms)
![Page 25: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/25.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
DCT
262,144 pixels 8353 largest terms, 3.2%(dropped 253,791 terms)
![Page 26: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/26.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Quantization
/
DCT Image Quantization Matrix
Quantized DCT Image
=
![Page 27: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/27.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Storage Order
![Page 28: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/28.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Error
error = abs(original – compressed) * 8
![Page 29: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/29.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Peak Signal-to-Noise Ratio
� Original Image (I) and new image (I’)
MSE =1N
N!
i=0
!I(i)" I !(i)!2
RMSE =#
MSE
PSNR = 10 log10
"I2max
MSE
#
= 20 log10
"Imax
RMSE
#
![Page 30: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/30.jpg)
!p" q!2 =
!"""#
"""$
(avg(pi)" avg(qi))2
(max(pi)"max(qi))2
(lum(p)" lum(q))2
· · ·
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Error Metrics
![Page 31: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/31.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Wavelets
![Page 32: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/32.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Haar Wavelets
Scaling function = average
Wavelet = difference
Transform:S = (A + B)/2D = (A – B)/2
Invert:A = S + DB = S – D
![Page 33: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/33.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Haar Wavelets
6 8 5 9 5 5 6 6
7 7 5 6
![Page 34: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/34.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Haar Wavelets
6 8 5 9 5 5 6 6
7 7 5 6 -1 -2 0 0
![Page 35: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/35.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Haar Wavelets
6 8 5 9 5 5 6 6
7 7 5 6 -1 -2 0 0
1 Transform Step
Averages• Smoothed version of signal• Lower resolution image
Differences• Local, high frequencies• Details missing from low resolution part
![Page 36: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/36.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Haar Wavelets
6 8 5 9 5 5 6 6
7 7 5 6 -1 -2 0 0
-1 -2 0 0
![Page 37: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/37.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Haar Wavelets
6 8 5 9 5 5 6 6
7 7 5 6 -1 -2 0 0
7 -1 -2 0 05.5
![Page 38: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/38.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Haar Wavelets
6 8 5 9 5 5 6 6
7 7 5 6 -1 -2 0 0
7 0 -.5 -1 -2 0 05.5
![Page 39: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/39.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Haar Wavelets
6 8 5 9 5 5 6 6
7 7 5 6 -1 -2 0 0
7 0 -1 -2 0 0
0 -1 -2 0 0
-.5
-.5
5.5
![Page 40: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/40.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Haar Wavelets
6 8 5 9 5 5 6 6
7 7 5 6 -1 -2 0 0
7 5.5 0 -1 -2 0 0
6.25 0 -1 -2 0 0
-.5
-.5
![Page 41: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/41.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Haar Wavelets
6 8 5 9 5 5 6 6
7 7 5 6 -1 -2 0 0
7 0 -1 -2 0 0
6.25.75 0 -1 -2 0 0
-.5
-.5
5.5
![Page 42: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/42.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Haar Wavelets
6 8 5 9 5 5 6 6
6.25 0 -1 -2 0 0
Full Transform
High Res DetailsMedium Res DetailsLow Res DetailAverage Value
-.5.75
![Page 43: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/43.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
2D Wavelet Transform
Standard– Apply full transform horizontally, then full
transform vertically– Creates long, thin basis functions – bad for
image compressionNon-standard
– Repeatedly apply 1 step horizontally, then 1 step vertically
– Creates square basis functions – good for image compression
![Page 44: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/44.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
What else needs compression?
VideoTextures (different requirements than plain
images)Geometry (including animations)Anything else?
![Page 45: CS148: Introduction to Computer Graphics and Imaging ...graphics.stanford.edu/.../cs148-09/lectures/compression.pdfCS148 Lecture 16 Pat Hanrahan, Winter 2009 Image and Video Data Rates](https://reader033.vdocuments.site/reader033/viewer/2022051905/5ff7dfd83f3e725f3714d474/html5/thumbnails/45.jpg)
CS148 Lecture 16 Pat Hanrahan, Winter 2009
Things to Remember
LosslessNo error, but not lots of compression
LossyError can be driven by human perceptionMore error, but lots of compressionDifferent error metrics (max, avg, perceptual)
Different Basis FunctionsJPEG / Discrete cosine transform (DCT)JPEG2000 / Wavelets