Lossless and near-lossless digital angiography coding using a two-stage motion compensation approach

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Computerized Medical Imaging and Graphics 32 (2008) 379–387

Lossless and near-lossless digital angiography codingusing a two-stage motion compensation approach

Rafael A.P. dos Santos, Jacob Scharcanski ∗Universidade Federal do Rio Grande do Sul (UFRGS), Caixa Postal 15064, 91501-970 Porto Alegre,

RS, Brazil

Received 23 July 2007; received in revised form 7 March 2008; accepted 18 March 2008

bstract

This paper presents a two-stage motion compensation coding scheme for image sequences in hemodynamics. The first stage of the proposedethod implements motion compensation, and the second stage corrects local pixel intensity distortions with a context adaptive linear predictor.he proposed method is robust to the local intensity distortions and the noise that often degrades these image sequences, providing lossless andear-lossless quality. Our experiments with lossless compression of 12 bits/pixel studies indicate that, potentially, our approach can perform 3.8%,

% and 1.6% better than JPEG-2000, JPEG-LS and the method proposed by Scharcanski [1], respectively. The performance tends to improve forear-lossless compression. Therefore, this work presents experimental evidence that for coding image sequences in hemodynamics, an adequateotion compensation scheme can be more efficient than the still-image coding methods often used nowadays.2008 Elsevier Ltd. All rights reserved.

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eywords: Angiography; Motion compensation; Context adaptive predictor

. Introduction

Several digital image compression methods have been pro-osed to address different applications. In applications whereome information loss is acceptable, lossy methods are oftensed, because these tend to be have higher coding efficiency.owever, in applications such as medical imaging, remote sens-

ng and legal imaging, the data validity and precision muste preserved for subsequent reconnaissance, therefore losslesspproaches tend to be more adequate.

Lossless image compression methods try to represent morefficiently the redundant information that often exists in images,t pixel and spatial levels (e.g. reducing the correlations amongpatially adjacent pixels in the coded image) [2,3]. Such meth-ds have been applied in static (still) images with success, andan be divided into three categories: transform-based methods,

ethods based on predictors, and multi-resolution techniques.chemes based on prediction alone, or in combination with otherpproaches (i.e. hybrid coders), have been successfully applied

∗ Corresponding author. Tel.: +55 51 3308 7128; fax: +55 51 3308 7308.E-mail addresses: [email protected] (R.A.P. dos Santos),

[email protected] (J. Scharcanski).

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895-6111/$ – see front matter © 2008 Elsevier Ltd. All rights reserved.oi:10.1016/j.compmedimag.2008.03.001

n lossless coding of still medical images, such as JPEG-LS [4]nd CALIC [5]. Besides, schemes based on context adaptive pre-ictive coding [1], and region segmentation [6], are interestinglternatives for still medical image coding. However, in someituations like medical functional imaging, dynamic images areore adequate. In these dynamic images the information redun-

ancy occurs in the spatial and in the temporal sense (i.e. pixelsn adjacent frames tend to be correlated to some degree). Thus,he compression techniques for videos often explore the spatialnd the temporal redundancy existing in the data (e.g. MPEG-27], H.264 [8] and others [9]).

High image resolutions and pixel depths often are usedn medical imaging, and the medical imaging studies usuallyre stored for long periods of time for legal reasons. There-ore, archiving (and/or transmitting) the large amounts of datanvolved in these studies has been challenging researchers inecent years [10]. The focus of our work is on lossless and near-ossless coding of imaging studies in hemodynamics, which cannvolve several lengthy image sequences (e.g. 200 frames each0 s). Roos et al. [11] showed that conventional video coding

echniques applied to hemodynamics series, trying to exploreemporal and spatial redundancies, had no advantage over stillmage coding techniques applied to these series frame-by-frame.

edical images, like angiographies, usually are stored and

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80 R.A.P. dos Santos, J. Scharcanski / Computerize

ransmitted using the DICOM standard. In fact, nowadays, mostICOM standard implementations code individually each frame

n a series, using other still image coding standards like JPEGossless, JPEG-LS and JPEG-2000 [12]. Video coding standardslso can be used (e.g. MPEG-2), but with less coding efficiencyas discussed before). Therefore, motion compensation tech-iques that have been successfully applied to generic videos, areot as efficient to code hemodynamics series, and other alterna-ives have been sought. The current trend is to code these frameeries in a multi-frame format. In other words, most currentpproaches focus only on the spatial redundancy of individualrames, and code them like they were still images.

Some of the reasons for not using motion compensation tech-iques, and take advantage of the temporal redundancy existingn hemodynamics series are: (a) the frames of these series cane very noisy, and most motion estimation techniques tend toenerate significant motion prediction errors; (b) strong bright-ess changes occur in corresponding pixels of adjacent frames,herefore the usual motion compensation assumption that objectolor/intensity remains constant is not valid here [13]. Theseocal brightness changes occur at the pixel level, caused by thehanges in X-ray transparency that take place when the injected

ontrast disperses in the patient blood stream (changing its den-ity), or when the patient internal organs move with respect toach other (e.g. during breath taking or heart beating). Fig. 1(a)nd (c) shows the initial frame of the first series of studies 1 and

srci

ig. 1. Study 1: (a) initial frame of the first series; (b) pixel intensity differences withntensity differences with respect to the next frame.

ical Imaging and Graphics 32 (2008) 379–387

, and the corresponding pixel intensity differences with respecto the next frame of those series are depicted in Fig. 1(b) andd). Most motion compensation techniques proposed for gen-ral purpose videos are not efficient in these image sequences14].

This paper presents a new context adaptive coding methodor image sequences in hemodynamics, based on the compen-ation of motion and local brightness/gray-level changes. Theroposed method is a two-stage context adaptive linear predic-or, which takes into account the local intensity changes andoise, common in these image sequences. It provides losslessnd near-lossless quality, and our preliminary experiments indi-ate that our approach potentially can offer lower bit-rates thantill image coding methods. In Section 2, we present our pro-osed method. The experimental results and some comparisonsith results obtained by different methods are shown in Section. Section 4 shows our conclusions and ideas for future work.

. Motion compensation for angiographies

In general purpose video coding, motion compensation haseen used to reduce the temporal redundancy in the video

equence by coding local differences between the correspondingegions of the scene. Most video coding techniques assume thatolor/intensity of the objects in a video are constant (or approx-mately constant) [15], and use sub-pixel approaches to make

respect to the next frame. Study 2: (c) initial frame of the first series; (d) pixel

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R.A.P. dos Santos, J. Scharcanski / Computerize

ore accurate estimates. However, this assumption is not validor hemodynamics series, as observed by Deuerling-Zheng etl. [16]. In fact, in these image sequences pixel intensity (gray-evels) changes are expected, even at locations that correspondn adjacent frames (see Section 1). Consequently, the motionstimation algorithms commonly used, such as block matching,ften find substantial matching block pixel differences in hemo-ynamics image sequences (i.e. large prediction errors) [17],nd tend to be not competitive compared to still image codingpproaches.

Therefore, to improve the motion compensation efficiencyn these image sequences, the pixel intensity changes occurringithin a context also must be compensated, as discussed next.

.1. Context adaptive motion compensation for imageeries coding

Our proposed method is a two-stage context adaptive linearredictor. Considering that predictions tend to be more accurateithin a defined context, the first stage selects image regions thatost likely correspond in adjacent frames (i.e. blocks in adjacent

rames), defining an adequate prediction context. Defined theontext, the second stage provides pixel predictions consideringhe actual pixel neighborhood in the previous frame (i.e. inter-rame prediction), and within the same frame (i.e. intra-framerediction), leading to smaller prediction errors than only usingntra-frame linear prediction.

A general overview of our method is the following:

Each frame k is divided in blocks Bi,k of size Nx × Ny.For each blockBi,k, we estimate its best matching blockBi,k−1in frame k − 1. Both blocks, i.e. Bi,k and Bi,k−1, determine thecontext for the next stage of our adaptive prediction scheme.An optimal linear predictor is obtained for the context speci-fied above.Finally, the residual prediction errors, along with the predictorand context parameters, are arithmetic encoded.

.2. Context selection

For the context selection, non-overlapping Nx × Ny blocks ofhe current frame (Bi,k) are matched with previous frame blocksy minimizing the absolute pixel intensity differences [18].

Fig. 2 illustrates the block matching process, where w is theearch window size, Bi,k is the ith-block of frame k, Bi,k−1 ishe corresponding block in frame k − 1 and (dx, dy) is the dis-lacement vector. It shall be observed that, experimentally, therediction errors between blocks Bi,k and Bi,k−1 can be sub-tantial because of local intensity changes. The next step of ouroding scheme tries to partially compensate for these gray-levelariations, noise and other local pixel changes, estimating anptimal linear predictor for a given context.

.3. Adaptive linear predictive coding

In this work, the current pixel intensity x(c) is predictedased on a set of its L neighboring pixel intensities x(c, i),

Tl

�t

Fig. 2. Block matching.

= 1, 2, . . . , L:

˜ (c) = w1x(c, 1) + w2x(c, 2) + · · · + wLx(c, L)

=L∑

i=1

wix(c, i), (1)

here x̃(c) is the prediction of x(c), x(c, i) is the ith neighboringixel, and wi is the ith linear predictor coefficient. The squaredrediction error for the current pixel x(c) is

(c) =[x(c) −

L∑i=1

wix(c, i)

]2

, (2)

nd for a set of ξ pixels, the sum of squared prediction errorsetween pixel x(c) and its prediction x̃(c) is given by

(c) =1∑

c=ξ

[x(c) −

L∑i=1

wix(c, i)

]2

. (3)

n matrix notation, let �t = [x(ξ), x(ξ − 1), . . . , x(1)]T be theet of pixels x(c), where c = ξ, ξ − 1, . . . , 1; and �w =w1, w2, . . . , wL]T be the linear predictor coefficients; and thequared prediction errors be �ε:

=

⎡⎢⎢⎢⎢⎢⎣

[x(ξ) − x̃(ξ)]2

[x(ξ − 1) − x̃(ξ − 1)]2

...

[x(1) − x̃(1)]2

⎤⎥⎥⎥⎥⎥⎦ . (4)

herefore, the linear prediction of the ξ pixel intensities (gray-

evels) can be written in matrix form as

= XT �w + �ε, (5)

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here X is the L × ξ matrix:

=

⎡⎢⎢⎢⎢⎣

x(ξ, 1) x(ξ − 1, 1) · · · x(1, 1)

x(ξ, 2) x(ξ − 1, 2) · · · x(1, 2)...

x(ξ, L) x(ξ − 1, L) · · · x(1, L)

⎤⎥⎥⎥⎥⎦ . (6)

he sum of squared prediction errors is now written in matrixorm as

T�ε = (�t − XT �w)T

(�t − XT �w). (7)

he set of optimal linear predictor coefficients �w, that minimizehe sum of squared prediction errors for �t, is determined by

aking the derivative of �εT�ε with respect to �w equal to zero:

∂�εT�ε∂ �w = 2X(�t − XT �w) = 0, (8)

r yet,

(�t − XT �w) = 0, (9)

nd,

XT �w = X�t. (10)

herefore, the optimal set of coefficients is given by

� = (XXT)−1

X�t, (11)

here the term XXT in Eq. (11) is

XT =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

ξ−1∑i=0

x(ξ − i, 1)2ξ−1∑i=0

x(ξ − 1, 1)x(ξ − 1, 2)

ξ−1∑i=0

x(ξ − i, 2)x(ξ − i, 1)ξ−1∑i=0

x(ξ − 1, 2)2

ξ−1∑ ξ−1∑

i=0

x(ξ − i, L)x(ξ − i, 1)i=0

x(ξ − 1, L)x(ξ − 1, 2) · ·

he autocorrelations in Eq. (12) can be made more explicit byenoting r(m, n) = ∑ξ−1

i=0 x(ξ − i, m)x(ξ − i, n), where m, n =ta

Fig. 3. (a) Block Bi,k at frame k; (b) corres

ical Imaging and Graphics 32 (2008) 379–387

·ξ−1∑i=0

x(ξ − 1, 1)x(ξ − 1, L)

·ξ−1∑i=0

x(ξ − 1, 2)x(ξ − 1, L)

ξ−1∑2

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

. (12)

, 2, . . . , L, and expressing Eq. (12) as

XT =

⎡⎢⎢⎢⎢⎣

r(1, 1) r(1, 2) · · · r(1, L)

r(2, 1) r(2, 2) · · · r(2, L)...

r(L, 1) r(L, 2) · · · r(L, L)

⎤⎥⎥⎥⎥⎦ , (13)

hich is a symmetric autocorrelation matrix.Finally, the term X�t in Eq. (11) is

�t =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

ξ−1∑i=0

x(ξ − i, 1)x(ξ − i)

ξ−1∑i=0

x(ξ − i, 2)x(ξ − i)

...ξ−1∑i=0

x(ξ − i, L)x(ξ − i)

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

, (14)

here x(ξ − i) is the pixel (ξ − i) of the training set �t, i.e. x(ξ −) = �t(ξ − i).

.3.1. Linear predictive coding adaptive to the context �tLet the set of ξ pixels in �t be the context for which an opti-

al linear predictor �w is designed, as described in Section 2.3.n this work, the optimal linear predictor is designed for theontext defined by Bi,k and Bi,k−1 according to the ordinaryeast squares criterion (OLS) [19](also see Eq. (11)). Our causaleighborhood is constituted by 12 pixels (i.e. L=12), three of

·i=0

x(ξ − 1, L)

hem are neighbors of xk at frame k, and the other nine pixelsre in the causal region of xk in the frame k − 1 (see Fig. 3).

ponding block Bi,k−1 at frame k − 1.

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Our experimental results are based on 106 series of 6 hemo-dynamics studies, using 12 bits/pixel and 8 bits/pixel. Studies 1through 6 contain 27, 16, 11, 21, 14 and 17 series, respectively.

R.A.P. dos Santos, J. Scharcanski / Computerize

Our method introduces an additional overhead when com-ared with the traditional block matching approach (i.e. for eachontext, 12 coefficients are coded as side information). How-ver, our method presents a more efficient code, because theptimal linear prediction reduces the prediction errors, makinghe overall bit-rate smaller.

.4. Encoding of prediction errors and coder parameters

For each block of frame k, the following data are obtained:he displacement vector (dx, dy) (referring to the block match-ng step); the prediction errors, i.e. the differences between theredicted and the actual pixel values of Bi,k; and the 12 linearredictor coefficients. The prediction errors and block predictorarameters are arithmetic encoded. Actually, the 12 linear pre-ictor coefficients wi=1,2,...,12 are real numbers wi ∈ [0, 1], buthey are represented as integers w

′i = �κ · wi� to improve cod-

ng efficiency. Our experiments showed that κ = 1000 providesgood compromise between coding efficiency of the linear pre-ictor coefficients, and the quality of the prediction obtainedith the approximation wi ≈ w̃i, where w̃i = κ · w

′i (i.e. when

oding or decoding the block data, the same approximation w̃i

f the linear predictor coefficients is used, instead of the wi

alculated by Eq. (11)).There are other information that also must be coded, so the

ecoder can reconstruct the data. In order to decide on a forward,ackward or bi-directional prediction scheme, these schemesere tested. The experimental results with angiography series

howed that all three prediction schemes obtain comparableesults, and forward prediction has been adopted in this work.onsequently, the first frame of a series has no antecessor, and

t is adaptively encoded using the method proposed by Schar-anski [1]. All other frames generate overheads, that are codeds lateral information, as discussed next.

The first pixel of the frame is coded based on its actualntensity value. Since the predictor uses previous column andine pixels in the causal region, the first line and the firstolumn of the image are encoded using the DPCM tech-ique (i.e. the difference between its value and the value ofhe previous pixel in the first line, or in the first column).or example, if the pixels in the first line (or first column)re [130, 128, 127, 132, 137, 133, 133, 127, 130, 129, . . .] theyre transformed to [130, −2, −1, 5, 5, −4, 0, −6, 3, −1, . . .]efore arithmetic encoding.

Some parameters used in arithmetic encoding also must beoded as lateral information (i.e. code length, symbol dictio-ary, and symbol count in the original data stream), becausehese will be needed to decode the data stream. These arithmeticoding parameters are Golomb encoded. In other words, an inte-er data stream Pj=1,2,...,S is Golomb encoded as Rj=1,2,...,S ,here Pj=1,2,...,S = �(Pj=1,2,...,S)/(M)� + Rj=1,2,...,S , and S is

he stream length. In this work, M = �E[Pj=1,2,...,S]� wassed. The Golomb coding parameter M is lateral informa-

ion and is coded with B bits as binary symbol. It waserified experimentally that, in all blocks and frames of theeries tested in our experiments, M can be binary encodedsing B = 11 bits. In our experiments, the chosen block F

ical Imaging and Graphics 32 (2008) 379–387 383

ize was 64 × 64 considering frame sizes of 512 × 512 pix-ls.

. Experimental results

ig. 4. Initial frames of the first series for: (a) study 1; (b) study 2; (c) study 3.

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384 R.A.P. dos Santos, J. Scharcanski / Computerized Medical Imaging and Graphics 32 (2008) 379–387

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Fig. 6. Comparison the experimental results obtained with the proposedapproach and other still image coding approaches (JPEG-LS, JPEG2000, theblock matching method proposed in [16], and the method proposed in [1]), forthe series in study 1: (a) 12 bits/pixel; (b) 8 bits/pixel.

ig. 5. Initial frames of the first series for: (a) study 4; (b) study 5; (c) study 6.

ll frames have a resolution of 512 × 512 pixels. Figs. 4 and 5llustrate the visual appearance of frames in these studies, show-ng the first frame of the first series for each one of the six studiessed in our experiments.

Figs. 6(a)–11(a) compare the bit-rates obtained by the pro-osed method in 12 bits/pixel series, JPEG-LS, JPEG-2000nd the method proposed by Scharcanski [1]. For 12 bits/pixeltudies our method obtains, on average, 6.79 bits/pixel, and per-

Fig. 7. Comparison the experimental results obtained with the proposedapproach and other still image coding approaches (JPEG-LS, JPEG2000, andthe method proposed in [1]), for the series in study 2: (a) 12 bits/pixel; (b)8 bits/pixel.

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R.A.P. dos Santos, J. Scharcanski / Computerized Medical Imaging and Graphics 32 (2008) 379–387 385

Fig. 8. Comparison the experimental results obtained with the proposedapproach and other still image coding approaches (JPEG-LS, JPEG2000, andthe method proposed in [1]), for the series in study 3: (a) 12 bits/pixel; (b)8 bits/pixel.

Fig. 9. Comparison the experimental results obtained with the proposedapproach and other still image coding approaches (JPEG-LS, JPEG2000, andthe method proposed in [1]), for the series in study 4: (a) 12 bits/pixel; (b)8 bits/pixel.

Fig. 10. Comparison the experimental results obtained with the proposedapproach and other still image coding approaches (JPEG-LS, JPEG2000, andthe method proposed in [1]), for the series in study 5: (a) 12 bits/pixel; (b)8 bits/pixel.

Fig. 11. Comparison the experimental results obtained with the proposedapproach and other still image coding approaches (JPEG-LS, JPEG2000, theblock matching method proposed in [16], and the method proposed in [1]), forthe series in study 6: (a) 12 bits/pixel; (b) 8 bits/pixel.

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386 R.A.P. dos Santos, J. Scharcanski / Computerized Med

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ig. 12. Experiments with study 3 using 12 bits/pixel using block matching atub-pixel resolution.

orms 3.8%, 2% and 1.6% better than JPEG-2000, JPEG-LSnd the method proposed in [1], respectively (see Table 1).ig. 6(a) also shows the bit-rates obtained using the informationentropic) block matching approach proposed by Deuerling-heng et al. [16], instead of the OLS approach (see Eq. (11)).

n all our experiments, OLS outperformed the entropic blockatching approach [16]. Sub-pixel block matching also has

eing tested, but in all our experiments our proposed methodas outperformed that approach (in average by 5.26%), and wasot included in Table 1. Fig. 12 illustrates the performance ofhe sub-pixel block matching method for study 3, and comparest with JPEG-2000, JPEG-LS, the method proposed in [1], andhe method proposed in this paper.

Near-lossless coding can be obtained by selecting lessits/pixel than the original pixel depth. Figs. 6(b)–11(b) showhe obtained bit-rates using only the 8 most significant bits in alleries of the 6 studies (out of the 12 bits/pixel). For 8 bits/pixeltudies, our method obtains, on average, 2.83 bits/pixel, anderforms 5.7%, 4.4% and 3% better than JPEG-2000, theethod proposed by Scharcanski [1] and JPEG-LS, respec-

ively (see Table 1). Particularly, Fig. 6(b) shows the bit-ratesbtained using the information (entropic) block matchingpproach [16], and it shows that OLS also outperformed thentropic block matching approach [16] when 8 bits/pixel wassed.

At a first glance, these gains could appear to be modest.ut, considering that in an average size hemodynamics service

everal studies are acquired per day (i.e. several patients arexamined each day), the resulting data volume can be substantialfter some time. Therefore, these coding gains imply in a sig-ificant economy of storage space. For example, coding only 6

ypical studies with JPEG-LS would require 1593 Mbytes, ver-us 1567 Mbytes with our method, providing an economy of6 Mbytes.

able 1omparison of the obtained bit-rates (bits/pixel)

o. of bits/pixel JPEG-2000 ICIP 2006 JPEG-LS Proposed method

8 BPP 2.99 2.95 2.91 2.8312 BPP 7.05 6.89 6.92 6.79

[

[

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ical Imaging and Graphics 32 (2008) 379–387

The experimental results indicate that our method presentsetter bit-rates for lossless coding of digital angiograms whenompared with state-of-the-art still coding methods. We attributehe coding gain to the reduced temporal redundancy resulting inur approach. A larger coding gain was obtained for 8 bits/pixelmages, and we credit this gain to the noise reduction in thesemages.

. Conclusions

We presented in this paper a context adaptive coding methodor hemodynamics studies, which uses a two-stage motion com-ensation scheme. The proposed method can provide losslessnd near-lossless quality, and our experiments indicate that ourpproach potentially can offer lower bit-rates than still imageoding methods that are representative in the state-of-the-art.ompared to motion compensation methods proposed specif-

cally for studies in hemodynamics, and to methods proposedor generic videos, our experiments suggest that our approachotentially can offer lower bit-rates.

As future work, we intend to develop lower complexity alter-atives for context definition and pixel intensity prediction,hat could lead to even lower bit-rates. Also, we would like totudy new methods for determining adaptively some of the cod-ng parameters that have been selected experimentally in thisork.

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international conference on image processing, ICIP, vol. 2. 2003. p.189–92.

afael Penna dos Santos has a M.Sc. degree in Computer Science (Federal Uni-ersity of Rio Grande do Sul, Brazil, 2007), and a B.Eng. in Electrical and Com-uter Engineering (Federal University of Rio Grande, Brazil, 2004). His mainreas of interest are image processing and analysis, and medical image coding.

acob Scharcanski has a Ph.D. degree in Systems Design Engineering (Uni-ersity of Waterloo, Canada, 1993), a M.Sc. degree in Computer Science (1984)nd a B.Eng. in Electrical Engineering (1981), both from the Federal Universityf Rio Grande do Sul (Brazil). His main areas of interest are image process-ng and analysis, machine learning and medical applications. He has lecturedt University of Toronto, University of Guelph, University of East Anglia andniversity of Manchester (UMIST), as well as in several Brazilian Universities.

e authored and co-authored more than 75 publications in Journals and Con-

erences. He also held research and development positions in the Brazilian andorth-American Industry. Currently, he is an Associate Professor at the Insti-

ute of Informatics, Federal University of Rio Grande do Sul, Porto Alegre, RS,razil.