Sonar Image Compression

Transcription

1 Sonar Image Compression Laurie Linnett Stuart Clarke Dept. of Computing and Electrical Engineering HERIOT-WATT UNIVERSITY EDINBURGH Sonar Image Compression, slide - 1

2 Sidescan Sonar Image Compression, slide - 2

3 Sidescan Sonar Applications Industrial Pipeline inspection Cable laying Mineral exploitation (gas, oil, diamonds) Sonar Image Compression, slide - 3

4 Sidescan Sonar Applications Environmental Fish stock monitoring Measurement of polar ice caps Sonar Image Compression, slide - 4

5 Defence Route surveying Object detection Sidescan Sonar Applications Sonar Image Compression, slide - 5

6 Why Compression? There are two applications for the compression of sidescan sonar data: Route survey database Compression of sidescan sonar surveys for use on board ship. AUV mounted sonar AUV's (autonomous underwater vehicles) carrying sonar transducers in contact with survey vessel via acoustic data link. Sonar Image Compression, slide - 6

7 Why Compression? There are two applications for the compression of sidescan sonar data: Route survey database Compression of sidescan sonar surveys for use on board ship. AUV mounted sonar AUV's (autonomous underwater vehicles) carrying sonar transducers in contact with survey vessel via acoustic data link. Sonar Image Compression, slide - 6

8 Image Compression Image compression seeks to reduce the amount of bytes required to represent a digital image, for increased storage capacity or transmission over a limited bandwidth channel. Image compression has become commonplace with the growth of the World Wide Web. A common compression technique is the JPEG (Joint Photographic Experts Group) standard, which uses the DCT (Discrete Cosine Transformation). The DCT is an example of a transform coding technique, that relies on the correlation that exists between image pixels. The DCT achieves compression by concentrating the signal energy into a relatively few coefficients. The more correlation between pixels, the fewer coefficients are required. Sonar Image Compression, slide - 7

9 The Discrete Cosine Transformation The Discrete Cosine Transformation: F( u, v) N N 2 1 = C( u) C( v) N 1 f ( x, y)cos (2x + 1) uπ (2y + 1) vπ cos 2N N x= 0 y= 0 2 The Inverse DCT: N N 2 1 f ( x, y) = N 1 C( u) C( v) F( u, v)cos (2x + 1) uπ (2y + 1) vπ cos 2N N x= 0 y= 0 2 where C( u), C( v) = 1 for u, v = otherwise Sonar Image Compression, slide - 8

10 Comparison of DCT Performance "Photographic" Image DCT Sidescan Sonar Image DCT f ( x, y) Sonar Image Compression, slide - 9

11 Comparison of DCT Performance "Photographic" Image DCT Sidescan Sonar Image DCT f ( x, y) F( u, v) Sonar Image Compression, slide - 9

12 "Photographic" Image Compression Sonar Image Compression, slide - 10

13 "Photographic" Image Compression Original Sonar Image Compression, slide - 10

14 "Photographic" Image Compression Original JPEG (15:1) Sonar Image Compression, slide - 10

15 Sidescan Sonar Image Compression Sonar Image Compression, slide - 11

16 Sidescan Sonar Image Compression Original Sonar Image Compression, slide - 11

17 Sidescan Sonar Image Compression Original JPEG (6:1) Sonar Image Compression, slide - 11

18 Compression of Sidescan Sonar Images The DCT performs poorly for sidescan sonar images as they contain relatively little correlation between pixels. This is due to the phenomena of coherent "speckle" inherent in the sonar imaging process. However, sidescan images contain a different type of redundancy: Sonar Image Compression, slide - 12

19 Route Surveying Sonar Image Compression, slide - 13

20 Texture Analysis Images are represented as a set of grey-level planes. Each grey-level plane is modelled as a spatial point process. Stochastic nature of textures can be represented by estimating statistics of quadrat counts Original image 256 grey-level planes Grey-level plane Sonar Image Compression, slide - 14

21 Route Surveying Sonar Image Compression, slide - 15

22 Seabed Mapping Sonar Image Compression, slide - 16

23 Object Detection Sonar Image Compression, slide - 17

24 Texture Synthesis One approach for texture synthesis is to model the texture as a random process: M-1 M f ( Assumptions: Stationarity Markovanity 0 1,..., M 1) = f f ( ( 0 1,, 1 2,...,,..., M 1 M 1 ) ) Sonar Image Compression, slide - 18

25 How to represent f ( 0, 1,..., M 1)? One approach is to use a multivariate normal pdf: 1 T 1 exp ( ) C ( ) 2 f,,..., ) = ( 0 1 M 1 M 2 where = M [ 0,..., 1] (2π ) C neighbourhood vector = [ x,..., x] mean vector C 2 σ c(1) =. c( M 1) c(1) σ 2. c( M 2).... c( M c( M σ. 2 1) 2) covariance matrix Sonar Image Compression, slide - 19

26 1: Normal Texture Synthesis A texture can be synthesised by first estimating the texture mean x, the variance s 2 and the autocovariance function c(.). At a particular location, the neighbourhood is computed and used to calculate the conditional mean value: cond = 1 R P( ) + The variance of the conditional distribution is independent of the neighbourhood : σ 2 cond =σ 2 PR 1 P T x where C = σ P 2 P T R Sonar Image Compression, slide - 20

27 Normal Texture Synthesis Results Brodatz "fur" texture Original Synthetic Sonar Image Compression, slide - 21

28 Comparison of Histograms Sonar Image Compression, slide - 22

29 2: k-nearest Neighbours Texture Synthesis To cater for non-gaussian textures, a non-parametric estimator may be used to represent the joint neighbourhood pdf f,,..., ). where ( 0 1 M 1 The k-nearest neighbours estimator was considered for this application, i.e. k f ( 0, 1,..., M 1) nv k is the number of nearest neighbours. V is the volume of a hypersphere centred on ( 0, 1,..., M-1 ). n is the number of samples. Sonar Image Compression, slide - 23

30 2: k-nearest Neighbours Texture Synthesis We can form the conditional pdf as: f ( 0, 1,..., f ( 0 1,..., M 1) = f (,..., k = nv k nv 1 V = V M 1 Where V 1 is the volume computed in the estimate of 1. This volume is constant for all values of ), hence we can write: f ( 1,..., M 1) 0 Sonar Image Compression, slide V M 1 ) ) f (,..., M 1)

31 Sonar Image Compression, slide : k-nearest Neighbours Texture Synthesis The conditional distribution function can be written as: We can sample this distribution to find a grey-level g 1, by using a random variable U, uniform in (0,1): The problem with this approach is that k-nearest neighbours is very slow for large data sets (such as images). = = = ),...,, ( ),...,, ( ),..., ( 0 N g g M g M M g V g V F ),..., ( ),..., 1 ( < M M g F U g F

32 Fast nearest neighbours search procedure k-nearest neighbours is best known in classification applications: class 1 class 2 unknown?? Two approaches: Hash tables Heckbert clustering Sonar Image Compression, slide - 26

33 Hash Table Searching? Sonar Image Compression, slide - 27

34 Hash Table Searching? Sonar Image Compression, slide - 27

35 Heckbert Clustering? Sonar Image Compression, slide - 28

36 Heckbert Clustering? Sonar Image Compression, slide - 28

37 Heckbert Clustering? Sonar Image Compression, slide - 28

38 Heckbert Clustering? Sonar Image Compression, slide - 28

39 Heckbert Clustering? Sonar Image Compression, slide - 28

40 Heckbert Clustering? Sonar Image Compression, slide - 28

41 Heckbert Clustering? Sonar Image Compression, slide - 28

42 Heckbert Clustering? Sonar Image Compression, slide - 28

43 k-nearest Neighbours Synthesis Results Brodatz "fur" texture Original Synthetic Sonar Image Compression, slide - 29

44 Comparison of Histograms Sonar Image Compression, slide - 30

45 Synthesis Results - Sonar Texture Original normal k-nn Sonar Image Compression, slide - 31

46 Synthesis Results - Sonar Texture Original normal k-nn Sonar Image Compression, slide - 32

47 Comparison of Histograms Normal Synthesis k-nn synthesis Sonar Image Compression, slide - 33

48 Image Compression using JPEG Original (65 kbytes) JPEG (6.5 kbytes) Sonar Image Compression, slide - 34

49 Image Compression Sonar Image Compression, slide - 35

50 Reconstruction with Normal Texture Synthesis Original (65 kbytes) Compressed (1 kbyte) Sonar Image Compression, slide - 36

51 Object Detection Sonar Image Compression, slide - 37

52 Comparison of Compression Schemes Sonar Image Compression, slide - 38

53 Comparison of Compression Schemes Original Sonar Image Compression, slide - 38

54 Comparison of Compression Schemes Original JPEG Sonar Image Compression, slide - 38

55 Comparison of Compression Schemes Original JPEG Compressed Sonar Image Compression, slide - 38

56 Compression with Texture Synthesis Original Compressed Sonar Image Compression, slide - 39

57 CONCLUSIONS Conventional image compression techniques (transform coding) are not suited to sonar images due to the speckle noise content. For route-survey purposes, sidescan images can be represented by the position and appearance of sediment textures and the position and appearance of objects. With this assumption, very high compression ratios can be achieved for sidescan sonar images. This method is only appropriate for textural data. Sonar Image Compression, slide - 40