ClassificatXon of D i g i t a l A n g i o g r a m s Using
M - u l t i p u l s e E x c i t e d l L i n e a r Prediction Model
S . Radhika U.C. Niranjan I.S.N. Murthy
Department of Elec, Engg., Indian Institute of Science, Bangalore INDIA.
Abstract- A new automated method is presented for the
classification of digital angiograms. The technique
is based on approximating the given image by a twodimensional linear prediction (LP) model along with
a multipulse excitation sequence, The input to the
synthesis filter is a stream of pulses, characterised
by their location and amplitudes. The pulse parameters are estimated by minimizing a least squares
problem, This results in a pulse pattern which
trave~sesthe contour of the dye in the angiogram.
Excitation of the model by this multipulse sequence
reconratructs the image containing only the dye
profille. The correlation between multiple frames can
be exploited in tracking the dye movements in time.
I. INTRODUCTION
Digital angiography is widely used in the
diaginosis and treatment of coronary arterial diseases. Identification of t h e path
traversed by t h e dye is an important image
understanding problem. Gray scale thresholding, knowledge based systems, neural
networks [l] and active contours [2] a r e
some of t h e image processing techniques
proposed in this direction. Each of these
tech:niques have a few inherent limitations
such as creation of a knowledge base,
network training and operator intervention
In this paper we propose a n automated
technique for classification of angiograms
into dye (arteries) and background, by
using a multipulse excited L P model.
11. THEORY
Th.e digital angiographic image s(m,p) is
represented as the output of a two-dimensional,, quarter plane linear prediction model
of order ( n , q ) excited by a white noise
sequence e(m,p), i.e.
s(m,p) = e(m,p)
t
n
I:
q
C a(k,r) s(m-k,p-r)
k=O r=O
(1)
where a(0,O) = 1. The parameters a ( k , r ) a r e
estimated by the covariance L P method.
Thle multipulse excitation a proximates
the residual e r r o r signal e ( m , p T in (1) by
a s e t of t l * t 2 pulses of amplitudes Bkr and
locations (nk,nr) as
u(m,p) =
tl-1 t2-1
C
I: Rkr G(m-nk,p-nr)
k=O
(2)
r:O
The output of the all pole synthesis filter
can then be written as,
tl-1 t2-1
s(m,p) = I:
I: Dkr h(m-nk,p-nr)
k=O r-0
A
..
0-7803-0785-2/92$03.OO OEEE
(3)
where h(m,p) is the impulse response of
t h e LP model. Simultaneous estimation of
pulse locations and amplitudes is a very
complicated and computationally expensive
problem. We overcome this problem by
separately estimating t h e location and
amplitude of one pulse at a time 131.
Minimization of the,sum of squared e r r o r
between s ( m , p ) and s ( m , p ) with respect to
t h e pulse amplitudes Bkr, results in t h e
normal equation,
a13 = c
(4)
where a is the autocorrelation matrix of
the model impulse response, c is t h e cross
correlation vector of s and h while 13 is a
vector made u p of unknowns I3
The resulting e r r o r in the estfmation of
t h e pulse amplitude vector is
N - 1 N-1
2
I: s (m,p)
m=O p=O
E = Z
-
DT c
(5)
Equation ( 5 ) is first used to locate the
pulse position by searching for the minima
in E for various lags of cross correlation
function c and (4) is then used to estimate
t h e pulse amplitude. This algorithm compu t e s one pulse at a time, positioning them
at those locations where the cross correlation between the model impulse response
and image is maximum.
When t h e auto and cross correlation
functions in t h e least squares normal
equation are mapped into r a s t e r sequential
form, the two dimensional estimation problem reduces to a single dimensional problem
and t h e optimal amplitude computation
algorithm in [3] can be used directly.
Since the maxima in cross correlation are
located at lags corresponding to dye position, t h e pulses are positioned along the
contour of the dye. Also excitation of the
model with
this multipulse sequence
results in a n image containing only the dye
in a clear background.
The proposed method of angiogram classification can be applied to t h e whole image
or on a block by block basis.
Mu I t iframe An a1ysis:
Both one shot and block by block
methods of classifications can be extended
for tracking the dye movement in a
sequence of angiographic images. The
pulses from the previous frame a r e used in
the estimation of pulses in t h e next frame,
and hence t h e movement of the dye in time
can be tracked.
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111. RESULTSAND DISCUSSION
Figs. l a and 2a show t h e original images
of size 128x128 quantized at 8 bits/pixel. A
block size of 32x32 and all pole models of
order 2 were used in the analysis. Figs. l b
and 2b shob the pulse positions as black
dots, superimposed on the originals for
comparison. Table I gives the number of
pulses u-hich a r e placed oatside t h e dye
contour in both the images. A s can be
seen, barring a few pulses, all a r e placed
along the d y e . Figs. I d and 2d give the
number of pulses used in each b:ock for
the two pictures. Figs. IC and 2c show the
respective model output responses. These
too give a good reconstruction of t h e dye
for
both the pictures. While t h e f i r s t
image i s a simple one the second one is
more complicated, containing a large amount
of vascuIature. The results indicate that
the algorithm has performed equally well in
both the cases.
T h e number of pulses reqciyed t o approximate an image depends iipor, the d e n s i t y
of dye. H o i v e v e ~the method can S e n;ac'e
independent of the number of ~ u l s e s h y
thresholding t h e erro:. E: in 1 5 ) iihich
would stop the idgorithm once a prespecified e r r o r power is reached.
pulse excited LP model is presented for
tracking dye movement in angiograms, with
highly satisfactory performance,
ACKNOWLEDGXZNT
We thank D r . T,V. Venkatesh and ? f r .
Ramani, Computer 1-ision Lab, Y r . Shashidhsra, Acoustics Lab and Y r . Sista, Image
Processing Lab, TISc for their help.
REFERENCES
El] R . Y e k o v e i , a n d Y. Stin, " C i a s s i f i c a ? i o n o f
d i g i t a l angiograms u s i n g arrificial neural
n e t w o r k s , " P r o c . IEEE E n g i n e e r i n g i n Medicine and
B i o l o g y S o c i e t , y , pp. 1 4 4 0 - 1 4 4 1 , 1 9 9 1 .
121 ?la
E. Hyke, Y . F. E z q u e r r a , D . L a w t o n , "L'asculat u r e d e t e c t i o n i n angiograms u s i n g a c t i v e contou r s , " Proc. IEEE Engineering i n Pfedicine and
B i o l o g y S o c i e t y , pp. 1054-1055, 1 9 9 1 .
[ 3 ] S . S i n g h a l , a n d 5 . S . Atal, " A m p l i t u d e O p t i m i z a t i o n and Fit.ch P r e d i c t i o n i n M u l t i p u l s e
Coders", I E E E Trans. ASS?, Vol. 3 7 , p p . 3 1 7 - 3 2 6 ,
?larch 1 9 8 3 ,
IV. coKcLL'sIopI
A fulIy automated method based o n multi-
F i g . 2a
Fig. la,2a:
O r i g i n a l Images;
Fig. 2c
F i g . 2b
ib,2b: Pulse positions
1c,2c
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::ode1
F i g . 2d
o u t p u t s ; 1 d , 2 d : Kumber o f pulses/block