Edge detection in JPEG2000 Wavelet Domain - Analysis on Sigmoid - - PowerPoint PPT Presentation

Edge detection in JPEG2000 Wavelet Domain - Analysis on Sigmoid Function Edge Model

MIE’2011, Oslo August 31, 2011 Vytenis PUNYS, Ramunas MAKNICKAS

• Dept. Multimedia Engineering

Kaunas University of Technology, LITHUANIA

V.Punys, R.Maknickas (KTU, LT) MIE’2011, Oslo

Whole Slide Imaging – dimensions & amount of data

¡ Typical:

20mm x 15mm @ .5µpp (“20X”) = 40,000 x 30,000 pixels = 1.2Gp = 3.6GB (uncompressed) 20mm x 15mm @ .25µpp (“40X”) = 80,000 x 60,000 pixels = 4.8Gp = 14.4GB (uncompressed)

¡ Extreme:

50mm x 25mm @ .1µpp (“100X”) = 500,000 x 250,000 pixels = 125Gp = 375GB (uncompressed)

l x 10 Z-planes => 3.75TB

V.Punys, R.Maknickas (KTU, LT) MIE’2011, Oslo

Automatical Scanning Systems

¡ 384 glass slides,

2-4 min./slide (20x-40x), 1 z-plane

¡ 20x: 69.1 Gbyte / 12.8 hours

40x: 276.5 Gbyte / 25.6 hours @ JPEG2000 compression factor 1:20

V.Punys, R.Maknickas (KTU, LT) MIE’2011, Oslo

Hierarchical Image Data Organisation

Image Size( Image1 ) 0.56 GByte Size( Image2 ) 23.8 GByte Label 539 x 507 Macro 1280 x 446 Thumbnail 1024 x 641 839 x 768 Intermediate 1 3247 x 2033 2 912 x 2 665 Intermediate 2 6 494 x 4 066 5 824 x 5 331 Hi-Res1 (20x/10x) 25 976 x 16 264 23 298 x 21 324 Hi-Res2 (40x) 93 194 x 85 298

V.Punys, R.Maknickas (KTU, LT) MIE’2011, Oslo

Research objective: quantification without image decompression

¡ What could be detected in compressed image

data structures (wavelet domain) using the bi-

• rthogonal wavelets defined in the JPEG2000

standard for lossless (CDF 5/3) and lossy (CDF 9/7) compression.

¡ The parameters of detected objects (e.g. edges,

their height and width) might be used for automatic cell quantification.

V.Punys, R.Maknickas (KTU, LT) MIE’2011, Oslo

Example of Microscopy Image (part of it)

V.Punys, R.Maknickas (KTU, LT) MIE’2011, Oslo

Wavelet coefficients (mapped to greyscale)

V.Punys, R.Maknickas (KTU, LT) MIE’2011, Oslo

Wavelet coefficients stored in JPEG 2000 format

V.Punys, R.Maknickas (KTU, LT) MIE’2011, Oslo

Wavelet coefficients “carry” information about signal magnitude and location …

Issues:

¡ Wavelets: compression / detection? ¡ DWT – de-correlation of information

l DWT coefficients “shifted” in space l DWT coefficients (value) depend on edge

magnitude and position

¡ Detection of areas or edges? ¡ JPEG 2000 process > DWT:

l Dyadic decomposition l Quantification of coefficients

V.Punys, R.Maknickas (KTU, LT) MIE’2011, Oslo

Edge model – sigmoid function

¡ Edge height

a

¡ Edge width

b

¡ Edge position

c (within the limits of decomposition)

. ) , , 2 ( ' ' ' ) , , 2 ( ' ' ' , ), 3 2 ln( 2 , 1 ) , , ( = = − > − = + = b a a f b a a f a c e b b a x f

a cx

V.Punys, R.Maknickas (KTU, LT) MIE’2011, Oslo

Back from wavelet coefficients to signal height and width

¡ Method 1: calculates parameters a and b of

all suitable edges, whose wavelet maximum coefficients at analysed scales are equal to given w. The result is the set of ranges [b1,b2]

• f width for every height a of an edge.

¡ Method 2 calculates detectable height

intervals [a1,a2] at various widths b of an edge.

V.Punys, R.Maknickas (KTU, LT) MIE’2011, Oslo

Modelling of edge detection M1: a=50 M2: a=150

V.Punys, R.Maknickas (KTU, LT) MIE’2011, Oslo

Number of “detected” edge heights

V.Punys, R.Maknickas (KTU, LT) MIE’2011, Oslo

Results (1/2)

¡ Achieved results are encouraging to

continue the research of edge detection in wavelet domain.

¡ Analysis showed different and

unambiguous correspondence of edge parameter vectors to wavelet coefficients.

¡ Variability of detected edge width for any

height does not exceed 0.5 pixel size for edges wider than 3 pixels.

V.Punys, R.Maknickas (KTU, LT) MIE’2011, Oslo

Results (2/2)

¡ M1 (“height first”) is more suitable for

lossy compressed images, and M2 (“width first”) – for lossless compressed ones.

¡ Naturally, detection results in lossless

compressed images are better than in lossy images, except the case when height of an object exceeds 150 – then the M1 is more accurate for height detection in lossy compressed images.

V.Punys, R.Maknickas (KTU, LT) MIE’2011, Oslo

Thank you for your attention

Any questions ?

?

Vytenis . Punys @ KTU . LT