translational motion compensation for coronary angiogram sequences

276 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 8, NO. 3, SEPTEMBER 1989

Translational Motion Compensation for Coronary Angiogram Sequences

Q. x. w u , P. J. BONES, MEMBER, IEEE, AND R. H. T. BATES, FELLOW, IEEE

Abstruct-A method of compensating for the lag of the video cameras typically employed in angiographic systems is presented for use in sequences of digitized X-ray images. The lag effect is reduced by a straightforward weighted subtraction which has the undesirable side effect of increasing noise. By superimposing several lag-corrected and appropriately shifted images, however, the signal-to-noise ratio can be restored. The algorithm presented uses the phase correlation method to measure the two-dimensional shift of a mobile coronary arterial structure. Processing is confined to a rectangular area of interest (AOI) which encloses a feature of clinical significance. The difference of the phases of the Fourier transforms of two frames is computed, combined with an appropriate filter, and inverse Fourier-transformed, to produce a phase-correlation image. The vector separation, from the origin of image space, of the peak of the phase-correlation image is our estimate of the shift of the artery’s position in the second frame as compared to the first. The isolation of the A 0 1 from the surrounding image is achieved by the application of a window and correction for any linear trend in the background intensity. The methods have been applied to both simulated coronary angiograms and actual data recorded during routine coronary catheterization. Applications for the methods include the generation of concentration versus time curves for blood flow estimation and the enhancement of images of critically narrowed portions of coronary arteries.

I. INTRODUCTION E report a new approach to processing sequences of coronary angiographic (CA) images, formed by im-

age-intensified X-rays after injection of a bolus of radio- opaque dye. Our methods are equally applicable to CA sequences where opacification is achieved by direct intra- arterial injection (IACA) and sequences following intra- venous injection (IVCA). The latter display significantly less contrast [ 11 than the conventional IACA images, but involve less risk to the patient [ 2 ] .

Digital subtraction angiography (DSA) [3]-[5] is perhaps the preferred method for imaging most of the body’s blood vessels, although it does not rival conventional ar- teriography for examining coronary arteries because the continuous and complicated motion of the heart prevents straightforward subtraction from being effective over the major part of an angiographic image [6]. This remains true when the recorded images are synchronized with either or both of the electrocardiogram [7] and the respi- ratory cycle [SI.

Manuscript received July 26, 1988; revised Febmary 28, 1989. This

The authors are with the Department of Electrical and Electronic En-

IEEE Log Number 8927703.

work was supported by the National Heart Foundation of New Zealand.

gineering, University of Canterbury, Christchurch, New Zealand.

We show here how to remove motion artifacts from sequences of CA images without resorting directly to DSA. Rather than attempting to enhance complete angiographic images, we compensate for motion only within a restricted region appearing in a sequence of images. We call this region an area of interest (AOI), which always encloses a segment of coronary anatomy of special clinical significance.

The theory underlying our processing is developed in Section 11. Modifications needed to compensate for var- ious defects of real world data are delineated in Section 111, while in Section IV we present examples of applying our procedures to computer-generated images and to clinical angiographic images. In Section V we assess the significance of our results.

11. THEORETICAL PRELIMINARIES Since it is now standard to obtain CA images from video

sources, the effects of video camera lag on the image of a rotating and translating object are examined in Section II-A. We demonstrate in Section II-B that, in the absence of all recording imperfections, weighted subtraction of successive CA images (exhibiting the effect of camera lag; see Fig. 1) provides a true image of an object which both translates and rotates. Four problems, which have to be considered if one wishes to process CA images optimally, are discussed in Section II-C. In Section II-D we intro- duce a technique, called phase correlation, which serves as a solution to the most important of the above problems when the object’s motion is purely translational. It can be advantageous, as we argue in Section II-E, to perform phase correlation before the subtraction procedure described in Section II-B. While phase correlation is fully effective only when the object translates uniformly, it can be expected to perform usefully for arbitrary translational motion even together with some slight rotation.

A . Effect of Video Camera Lag

The video cameras in most coronary angiography systems are of the vidicon or plumbicon types, both of which exhibit appreciable “lag,” i.e., once excited, a spot on the camera target screen persists for tens or hundreds of milliseconds [9], [ 101. Table I lists the exponential decay constants for several commercial camera systems. The image-intensifier is excited each time the X-ray tube is pulsed. Consequently, the image appearing on the camera

0278-006218910900-0276$01 .OO 0 1989 IEEE

WU et al. : CORONARY ANGIOGRAM SEQUENCES 211

Fig. 1. Four 128 X 128 pixel images of a coronary artery phantom (dye- filled cylindrical hole in a block of perspex): (a) and (b) consecutive frames during motion (translation at constant velocity) of the phantom towards the top left corner; (c) phantom stationary; (d) after application of ( 3 ) to the images (a) and (b) with k = 0.7.

TABLE 1 SOME TYPICAL VIDICON CAMERA LACS

Camera Vidicon Vidicon Vidicon TY Pe (normal) (lead oxide) (multilayer)

Persistence after 200 rns 15 percent 2.0 percent 8.0 percent

target screen is effectively a multiple exposure. It is as- sumed here that one image (i.e., digitized video frame) is obtained for each X-ray pulse. When the object moves during recording, the resultant images are noticeably blurred, as illustrated in Fig. 1. Fig. l(a) and (b) shows two sequential CA images of a dye-filled coronary phantom recorded while the phantom is moving. Fig. l(c) shows a CA image of the same phantom when it is stationary. Note that camera lag has caused a significant blurring of the edges in Fig. l(a) and (b) as compared to (c).

Consider a sequence of “ideal” CA images, uncontam- inated by recording noise or any other distortion. We take km,n to denote the fraction of intensity, due to the ( m - n)th X-ray pulse, persisting on the target screen at the instant of the mth pulse; implying that km,o = 1 for each m. Also consider an object which translates and rotates while the image sequence is recorded, with a ( & ) being the true image of the object (i.e., what would always be recorded if the object was stationary and if the target screen exhibited no lag), where g is the position vector of an arbitrary point in image space. Denoting the translation and rotation of the object (with respect to any fixed axes), at the instant of the mth X-ray pulse, by the shift 8, and the dyadic R,, respectively, we see that the mth CA image f m ( x ) can be expressed as

m

f r n ( X ) = C km,na(Rm-n * (X + S m - n ) ) . (1) n=O

Morse and Feshbach [ 111 explain the properties and uses of dyadics. In practice, X-ray tubes are regularly pulsed. The video frames are also recorded periodically. Here we

take the X-ray pulse repetition frequency to equal the video frame rate, implying that,

km.n = v ( 2 ) where k = k, , , is a constant for a given video camera (refer to Table I).

In practice, k may be estimated by observing the re- sponse of the camera to a step change in X-ray intensity. We found that the simplest method was to record a sequence of images of uniform phantom material and record the video signal immediately following switching off the X-ray generator. The mean intensity of a region of the center of each digitized frame was then plotted as a function of time and k estimated by curve fitting.

B. Subtraction of Successive CA Images We see from (1) and (2) that

which confirms that weighted subtraction of successive CA images produces a true image of the object. This image is translated (i.e., shifted) by zm + and is rotated by the angle implicit in R, + I . Fig. l(d) illustrates the result of applying (3) to the images shown in Fig. l(a) and (b).

While this subtraction operation often reveals detail that is barely apparent in unprocessed CA images, the version of the true image so generated tends to be distinctly noisy [see Fig. l(d)] [12]. The problems which must be solved to produce more faithful images are outlined in the next subsection.

C. Exposure, Enhancement, Registration, and Ancillary Motion Problems

It is difficult to expose different CA images identically for many reasons, perhaps the chief being the variable intensity of the X-ray pulses. This implies that the mth CA image is notfin(&), as defined by (l) , but (ern f m ( x ) ) , where the mth exposure e, varies in general with m. The solution to this exposure problem is to multiply the rnth CA image by a constant before performing the subtraction operation described in Section 11-B and, then, to vary this constant until the outcome of the subtraction is “most like” the image of a single object. Because such compensation for variable exposure can never be perfect, the re- sidual unwanted detail in the subtracted images consti- tutes a species of noise, which adds to all the other forms of contamination that manifest themselves in practice.

Given a sequence of CA images, we perform many exposure-compensated subtractions, each of which gener- ates a noisy version of the true image of the object. To obtain an improved image we must contrive means of en- hancing these noisy versions. The obvious solution to this enhancement problem is to appropriately superimpose all of the noisy versions.

Superimposing the noisy versions is only effective if the detail representing the object in each version is registered such that this detail is reinforced when the versions are


superimposed. To solve this registration problem we need to deduce the rotations and shifts experienced by the object between the instants at which the X-ray tube is pulsed. The next subsection presents a solution for an object whose motion is purely translational.

The subtraction operation described in Section II-B does not suffer only from the exposure problem. There is also the problem of ancillary motions which are due to the im- possibility of perfectly maintaining the juxtaposition of the patient and X-ray apparatus while a sequence of CA images is recorded. The implication here is that the mth CA image is not even ( e , f m ( x ) ) but is more nearly ( e, f , ( T, [ x + t, ] ) ) , where the dyadic Tm and the vector I , characterize the rotation and shift due to the ancillary motion. Since neither the T, nor the t, are known, they must be eliminated before the subtractions can be performed successfully. A partial solution to this ancillary motion problem is presented in Section II-E.

D. Phase Correlation For a purely translating object (i.e., the motion is such

that each R, is the unit dyadic), the outcome of the subtraction operation described in Section II-B is, in the absence of any of the imperfections which are manifested in practice, what we call the (m + l ) th translated version a?, + I (x) of the object's true image

arn+l(x) = a ( & - s m + l > * (4)

We now adopt the notation a ( ? ) tf A ( g ) to identify A ( U ) as the spatial frequency spectrum of a (g), with the Fourier transform convention used in [13, sect. 61 being understood, where U is the position vector of an arbitrary point in Fourier space. Note that wherever the computa- tion of Fourier transforms is mentioned in this paper, the fast Fourier transform (FFT) algorithm [13, sect. 121 is implied.

On defining a,(&) tf A,,,(&), we see from (4) and the shift theorem for Fourier transforms [ 141 that

A , ( & ) = A ( & ) exp ( i27~g - s-) ( 5 )

where i = a. It follows from ( 5 ) that

%7+'1(14) = Phase{4n+l(k!)) - Phase{~, , (u) )

= 27TU * [ S m + l - & I . (6) Ideally, inverse Fourier transformation of exp ( i + ( U ) ) yields 6(x - girl + I + sffl ), where 6 ( . ) de- notes the two-dimensional delta function [ 13, sect. 61, implying (naively) that the shift ( sm + - 3 , ) can be re- covered with arbitrary precision. In practice, of course, the spatial frequency content of A ( U ) is limited, effectively restricted to some finite part of Fourier space. So, we form the composite spectrum

C(U> = W(U> exp ( i+(U>) (7) where W ( g ) is a real, nonnegative, symmetric "window" having a value close to unity throughout most of the aforementioned part of Fourier space but falling

smoothly to zero at its perimeter. Defining c ( 5 ) * C ( U ) , it is seen that c (x) has the character of an impulse of finite width centered at x = 5, + - g,. The term "phase correlation" was given by Kuglin and Hines [15] to this method of determining the translation between two images.

We emphasize, in agreement with others [16], [15], that r ( 5 ) tends to be more sharply peaked than the cross-correlation of arrr + (g) and arrr (g) . The point is that the effective width of W ( g ) can be usefully chosen to be wider than the central lobe of I A ( U ) 1 2 . E. Towards Solution of the Ancillary Motion Problem

In order to solve the ancillary motion problem introduced in Section II-C, we must determine each of the T, and f m . It is equivalent, and more convenient, to find the total rotation and shift that the object experiences between each pair of successive X-ray pulses. Accordingly, we take T,,, and t, to be incorporated into R,, and E,,,, as defined in Section II-A. We can claim to have solved the problem when R, + I R,' and ( S, + - s,) have been determined for each m. While we do not consider the determination of rotation here, we demonstrate that its presence need not prevent useful estimation of translational motion.

On defining f m (5) * F,,, ( U ) , and recognizing that g ( R . g) + G ( R . U ) for arbitrary g ( x ) * G(g) and any rotation dyadic R , we see from (1) and (2) that

F,(g) = c knA(R,-, . U ) exp (i27rR,-, . U m

s ~ - , ) n=O

so that

F , + l ( U )

= F,(U) exp . [$,+I - S,l) m

+ C k n [ ~ ( ~ , , , - , * exp ( i 2 a ~ , + ~ - , n = O

* U & + I - , )

- A ( R , - , E ) exp ( i 2 7 ~ [ ~ , , - , , g g m - ,

+ k"+'A(R" * 4 1 ) . ( 9 )

+ U . Sm+l - U * zm1)]

It seems there is no benefit to be expected in general from attempting to interpret the difference of the phases of F , + , ( g ) and F,(u) in the same way as we interpret +,,+ ( U ) in Section II-D. On the other hand, when k is small enough, and the differences between R, + and R, are sufficiently slight (for any n ) , one sees that the first term on the right-hand side of (9) may dominate the final term (the latter tends to be negligible when m exceeds, say, 3 or 4 ) . It seems reasonable to expect, therefore, that phase correlation can provide a useful estimate of (5 , +

WU et al.: CORONARY ANGIOGRAM SEQUENCES 219

- 3,) for some arbitrarily translating and slowly rotating objects (i.e., objects which rotate by no more than a small angle between any two frames). Fig. 4 illustrates the shift

mated by phase correlation. Note further that, when the motion is purely transla-

tional (i.e., there is no rotation implying that each Rm is the unit dyadic), and m is large enough for the final term on the right-hand side of (9) to be negligible, (9) reduces to

cess each image by an algorithm which subtracts a linear function A(g) from all pixels within the AOI, where

( 12) of a nonuniformly translating object being correctly esti- A(&> = YXx + YyY + K

with A,, A,, and K estimated by linear regression of the CA image intensity function within the A01 on the coor- dinates (x, y ) . We find that, in addition to improving the performance of the phase correlation algorithm, this linear background subtraction leads to a significant improvement in the visibility of the artery in the AOI. (Note that this particular subtraction process does not add to the noise level of the image.)

B. Ameliorating Effects of Image Truncation Ideally, in each CA image, the A01 contains the whole

of the FOI and no part of any other cardiac feature (which can in general be expected to be executing a different motion from the FOI). In practice, of course, parts of other features cannot be prevented from appearing within the AOI in images, nor can all of the FOI always be present within the AOI. So, significant cardiac features,

Frn+I(ii) = Frn(g) ~ X P (i2au - & I ) m

+ k”A(g)[exp (i2ag * s , + ] - ~ )

-

n = l

(i2au * [ s rn -n -t 3 m + ’ - hl)l’ ( 10)

In the particular case of uniform translational motion, for which

where 5 is a constant shift, the summation in (10) van- ishes. It follows that the capability of phase correlation to estimate the shift between successive CA images of a uniformly translating object is unaffected by the images being multiple exposures.

Ill . PRACTICAL IMPLEMENTATION The processing introduced in Section II is ideal in the

sense that it takes no account of the imperfections of CA images peculiar to clinical environments. After describing appropriate modifications and extensions of the idealized processing in Sections 111-A, 111-B, and 111-C, we present in Section 111-D a practical image processing algorithm, which is illustrated in Section IV.

The goal of the processing is to obtain an enhanced image of a feature of interest (FOI, usually a particular section of artery) present in a sequence of CA images. We select a restricted area of interest (AOI) enclosing the FOI throughout the sequence. For practical computational reasons the A01 is chosen to be a rectangle, of a size appropriate for the FOI, with its sides parallel to those of the camera target screen.

A. Compensating for Background The arterial segment to be imaged is not the only struc-

ture causing intensity variations across the AOI of a CA image. The other intensity variation, or “background,” is due to the heart muscle itself, the blood mass within the heart and the overlying ribs. This background often dominates the FOI within the AOI and does not always move together with the FOI. It tends to manifest itself as a relatively smooth featureless variation across an AOI, approximating a linear gradient in x and y .

We find that phase correlation is adversely affected by the presence of linear background. We therefore prepro-

both of interest and otherwise, are in general truncated by the rectangular perimeter of the AOI.

There are two proven techniques for ameliorating the effects of truncation. They are “edge-extension’’ [ 13, sect. 151 and “windowing” [17], [18]. While the former is often more efficacious, the latter tends to be more straightforward and we find it adequate for angiographic processing because the effects of background and noise are in our experience more severe than those of truncation. Note that windowing performs two roles here. First, it reduces the effects caused by the A01 encompassing overlapping, but different, portions of the image, as ob- served by Alliney and Morandi [17] (cf. [18]). Second, it reduces “spectral leakage,” which results when the FFT is applied to nonperiodic data [ 191. Consequently, provided the major degradations due to truncation are prevented, which they are by windowing, no further sophis- tication is warranted.

Before submitting the CA images to phase correlation, we apply a Hanning window [19] to the contents of the AOI in each CA image.

C. Compensating for Noise Noise in a digitized angiographic image is added at each

stage of the generation and capture of the image. Quan- tum noise, caused by the limited and Poisson-distributed number of X-ray photons incident per unit area per frame of the CA image sequence, usually predominates [20] . Secondary sources of additive noise include electronic noise within the video chain (significant when a video tape recorder is used as an intermediate image store) and the imperfections introduced in: a) scanning the image in the video camera and; b) quantizing the video signal for digital storage [3]. Our studies show that the noise has a frequency spectrum which is essentially “white.” Since the spectrum of a noiseless image of a typical FOI is, however, concentrated at low frequencies (i.e., near the origin


am+ 1, a

m=l ...( M-1)

Fig. 2 . Block diagram of the three sections of the motion compensation algorithm: (a) lag compensation ( m = 1 . . . (A4 - 1 ) ) ; (b) phase correlation (rn = 1 . . . (A4 - 2 ) ) ; (c) averaging with shift correction ( m = I ’ ’ . ( M - 1)) .

in Fourier space), the form of the window function W ( U) introduced in (7) is quite critical. Our computational experience has led us to choose the circularly symmetric Blackman window [ 191.

D. A Practical Image Processing Algorithm

The given sequence of CA images (containing some number, here denoted by M , of individual images) is processed in the following series of steps (refer to Fig. 2). The result of each step is indicated by the item to the right of the symbol ‘‘3”.

1) The A01 is chosen to encompass the FOI throughout the sequence, thus, forming a sequence of truncated images = fm , m = 1 . . . M .

2) Each pair of images fm and f m + l , m = 1 * . . ( M - 1 ) are combined as prescribed by ( 3 ) , compensating for multiple exposures * a, + m = 1 . . . ( M - 1 ).

3) The linear background is subtracted from each image am+, , m = 1 * . . ( M - 1) * uk’i l , m = 1 * * *

( M - 1). 4) Each image a : i l , m = 1 . ( M - 1) is win-

dowed = )a ,+ l , m = 1 . . . ( M - 1). 5 ) Phase correlation is performed for each consecutive

pair of images a 2 i and to estimate relative shift vectors * ( ~ 2 ; ~ - sg!,), m = 1 . .

6) A single image d is computed by summing the ( M - 1) images a,.,, m = 1 . * . ( M - 1) with appropriate shifts [refer to Fig. 2(c)].

( 2 )

( M - 2) .

IV. ILLUSTRATIVE EXAMPLES In this section we present results of applying our algo-

rithm (Section 111-D) to computer-generated images (Sec- tion IV-A below) and CA images obtained under practical clinical conditions (Section IV-B) .

A. Computer-Generated Images

Figs. 3-5 are results of computer simulations. The X-ray shadow image of a coronary artery (or, more spe- cifically, the dye within the lumen of the artery) was simulated by calculating the projection of two intersecting homogeneous circular cylinders according to the exponential law of attenuation. The cylinders are embedded in a homogeneous region of lower attenuation.

Fig. 3 shows the phase difference function @(U) calculated twice for a pair of computer-generated images. The second of the pair was translated up and to the right. The phase difference shown in Fig. 3(a) was calculated without windowing (i.e., the images were simply truncated at the edge of the AOI), whereas a circularly symmetric Hanning window was applied to the original images in calculating Fig. 3(b). Clearly, Fig. 3(b) shows the expected triangular plane wave appearance predicted by (6), remembering that phase is constrained within the range -7r to +-n.

Fig. 4 indicates that the presence of significant video camera lag ( k = 0.6 in this example), simulated by making each image a multiple exposure (with the object in nonuniform translation), does not prevent an accurate detection of shift (as argued in Section 11-E). Note how the presence of noise in the original images causes the phase difference in Fig. 4(c) to become noisy except near the origin. Combination with the Blackman window function before inverse transforming ensures that a single promi- nent impulse, albeit of finite width, appears in the phase correlation image [Fig. 4(d)].

Fig. 5 illustrates the effect of slight rotation as well as translation on the phase correlation process. The phase difference + ( U ) is shown in preference to the phase correlation, since it is the nature of + ( 4 4 ) near the origin (i.e., the center of each image) which determines the position of the phase correlation peak. The original computer-generated images were of the same form as those shown in Fig. 4(a) and (b), except that they were “single exposures” and noiseless. Gradual stretching and distortion of + ( U ) can be seen near the origin as the rotation increases from 3” through 6”. After inverse transforming, the correct translation was detected for cases (a) and (b) in Fig. 5 , but not for (c) and (d), i.e., for up to 4” rotation.

B. Clinical CA Images

We have successfully applied the lag removal and phase correlation methods to a number of CA images. A single illustrative example of the application of the complete algorithm defined in Section 111-D is presented in Fig. 6. A sequence of nine consecutive frames of an A01 positioned

WU e1 a/ CORONARY ANGIOGRAM SEQUENCES 28 1

Fig. 6. Averaging of a sequence of CA images: (a) the first of a sequence of nine consecutive frames of the right coronary artery; (b) the same frame as shown in (a) after lag correction; (cl average of the nine frames with correction for the shifts computed by phase correlation; (d) average

within the AOI.

(a) (b) Fig. 3. Effect of windowing on the compensation of the phase difference

Q ( U ) (6): (a) @ ( 5 ) computed from two noise-free computer-generated

symmetric Hanning window to the same images. 64 64 pixel images; (b) ‘ ( U ) computed after applying a circularly of the 16 frames without correction for the significant shifts of the artery

Fig. 4. Phase correlation of‘ noisy multiple exposures: (a) and (b) are consecutive images multiply exposed according to (1) ( k = 0.6), with nonuniform horizontal translation simulated (the x component of :,?, ~ ,) var- ied sinusoidally); (c) phase difference between the Fourier transforms of (a) and (b); (d) phase correlation, with the peak indicating the shift between a ( ? + 2,fl) and u (: + T,,~ - , ).

Fig. 5 . Effect of rotation on the phase correlation method of translation detection. The phase difference + ( E ) is shown computed for two noise- free computer-generated images with identical translation but increasing rotation: (a) 3”; (b) 4 ” ; (c) 5”; (d) 6 ” . In this example inverse Fourier transformation resulted in the correct translation being dctected in cases (a) and (b) only, i.e., with up to 4” rotation.

over the right coronary artery is averaged both with [Fig. 6(c)] and without [Fig. 6(d)] correction for shift. The first original frame in the sequence is shown in Fig. 6(a) and the same frame, after lag removal, is shown in Fig. 6(b). While both averaged images show reduced noise levels, the motion has clearly blurred the features of the artery in Fig. 6(d). When the averaging is performed with correction for shift [Fig. 6(c)] the artery is seen positioned as in

Fig. 6(a). A significant improvement in signal-to-noise ratio is demonstrated.

V. CONCLUSIONS We have introduced a straightforward method of reduc-

ing the effect of video camera lag (which tends to make each frame a multiple exposure) on the sharpness of digitized images of the coronary arteries. The method makes no assumptions about the nature of the coronary arterial motion and an easily-implemented method of estimating the “lag factor” k is suggested. Our results indicate that the method is effective in its objective, but causes a significant worsening of the signal-to-noise ratio (SNR). Su- perimposing several (appropriately shifted) lag-corrected frames allows the SNR to be restored, provided that the translation can be accurately determined. The noisiness of the lag-corrected images restricts the choice of methods for translation detection. The application of edge enhancement as a preprocessing step in the power cepstrum method reported by Lee et al. [21], for example, could not be expected to produce sensible results here. Rather we have taken pains not to further worsen the SNR in our preprocessing (hence, the use of linear background subtraction). Let us now consider the effect of averagin on SNR. Averaging of N frames can give at best a d i m - provement in SNR. Making the (reasonable) assumption that the image noise is uncorrelated between frames and that the effects of background structures are minimal, averaging with or without shift correction will achieve sim- ilar reduction in the noise level. However, the use of shift correction has (at least) three advantages: 1) (most im- portantly) the FOI is not distorted as it would be without alignment; 2) background structures which are stationary are “softened” by their (misaligned) averaging; and 3) background structures which are moving with the FOI are less likely to be smeared over the FOI and obscure it, as is clearly evident in Fig. 6(d).

We have confirmed the finding of others [ 161, [ 151 that the phase correlation method of shift detection is a viable alternative to straightforward correlation. Further, we have shown how the method can be invoked for a small isolated A01 within a sequence of images and remain ac-


curate even when video camera lag causes each frame to be a multiple exposure. The main advantage of this approach over conventional correlation is its improved res- olution, in that it can estimate shifts more accurately, because the peak of c(x_) is narrower than that of the correlation function. Like correlation, our method could be readily and inexpensively implemented in hardware, the most demanding operation being the two-dimensional FFT. The multiplication of the input images by the Han- ning window and the filtering of noise are operations which could be performed efficiently by array-processing circuitry. When a sequence of consecutive frames is being processed, peak detection could be accelerated by first searching that part of the output where the peak was detected when processing the previous pair of frames. Note that the shift can be resolved to better than to the nearest pixel. State-of-the-art integrated circuitry could, we be- lieve, process sequences of 128 x 128 pixel A01 frames with our algorithm at a rate of more than 5/s, even though our present preliminary implementation of the method on a VAX 750 (programmed in Pascal) takes approximately 30 s per 64 X 64 pixel frame.

Several assumptions concerning the motion of the arterial structure within an A01 have to apply for phase correlation to be useful. The requirement for minimal rotation (our results and those of De Castro and Morandi [ 181 indicate that less than approximately 3” rotation is toler- ated) from each frame to the next is not met by many regions of a typical coronary angiogram. Parts of the arteries buckle as the epicardial surface to which they are attached contracts and distorts. In addition, two arteries whose projections onto the two-dimensional image are close together may physically lie on different regions of the epicardium. One artery may therefore appear to move independently of the other within the AOI. However, the X-ray angiographic apparatus may be rotated to get different projections of each coronary artery. At least one projection normally minimizes the effects of buckling of the arterial segment of interest while keeping that region of the image clear of over- or underlying structures. Thus, choosing the best projection for a given arterial feature can allow phase correlation to be usefully applied. Clearly, significant rotation also degrades the averaging process. For this reason we are pursuing, as are others [ 181, [2 11, methods of accurately determining rotation to augment the algorithm reported here.

The arterial segment within the A01 may be suspected of including a critical stenosis of which a sharper image is required, or it may be a monitoring point for obtaining concentration versus time curves for flow determination [22], [23]. In both situations, averaging of successive frames can produce a sharper image if the frames are over- laid so that the segment is in the same location in each shifted frame. Furthermore, following the motion of an arterial segment leads to an improvement in the accuracy with which dye concentration within an artery can be estimated because the effects of surrounding tissue are sig-

ACKNOWLEDGMENT The authors gratefully acknowledge the assistance and

interest of the staff of the Department of Cardiology, The Princess Margaret Hospital, Christchurch, New Zealand, especially Dr. H. Ikram and Dr. M. Richards.

REFERENCES N. Eigler, J. M. Pfaff, J. Whiting, T. Nivatpumin, and J . S. Forres- ter, “The role of digital angiography in the evaluation of coronary artery disease,” Int. J . Cardiol., vol. 10, pp. 3-13, 1986. F. E. Maddison, “Patient evaluation and other clinical considera- tions,” in Vascular Surgery, R. B. Rutherford, Ed., First ed. Phil- adelphia: Saunders, 1977, pp. 251-254. D. C. Levin, R. M. Schapiro, L. M. Boxt, L. Dunham, D. P. Har- rington, and D. L. Ergun, “Review: DSA: Principles and pitfalls of image improvement techniques,” Amer. J . Roentgenol., vol. 143, pp. 447-454, 1984. D. F. Guthaner, L. Wexler, and B. Bradley, “Digital subtraction angiography of coronary grafts: Optimisation of technique,” Amer. J . Roentgenol., vol. 145, pp. 1185-1 190, 1985. H. G. Bogren and J . M. Bursch, “Digital angiography in the diagnosis of congenital heart disease,” Cardiovasc. Intervent. Radiol.,

0 . Ratib and W. Rutishauser, “Recent developments of cardiac digital radiography,” Int. J . Cardiac Imaging, vol. 1, pp. 29-39, 1985. H. G. Bogren, B. M. T . Lantz, R. R. Millar, and D. T. Mason, “Effect of respiration on cardiac motion determined by cineangiog- raphy,” Acta Radiol. Diagnosis, vol. 18, pp. 609-619, 1977. D.-W. Ro, “Retrospective gating of masks in digital subtraction imaging of coronary arteries,” Dep. Radiol., Univ. Pennsylvania, Tech. Rep. MIPG102, 1985. B. G. Batchelor, D. A. Hill, and D. C. Hodgson, Automated Visual Inspection. J . A. Garrett and P. H. Smithson, “Conventional X-ray imaging,” IEEProc., vol. 134, pt. A, pp. 107-114, 1987. P. M. Morse and H. Feshbach, Methods of Theoretical Physics. New York: McGraw-Hill, 1953, pp. 54-73. S. Balter, D. Ergun, E. Tscholl, F. Buchoeven, and L. Verhoeven, “Digital subtraction angiography: Fundamental noise characteris- tics,” Radiol., vol. 152, pp. 195-198, 1984. R. H. T. Bates and M. McDonnell, Image Reconstruction and Res- toration. Oxford: Clarendon, 1986. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. New York: McGraw-Hill, 1978. C. D. Kuglin and D. C. Hines, “The phase correlation image alignment method,” in Proc. Int. Con$ Cybern. Society, 1975, pp. 163- 165. E. De Castro, G. Cristini, A. Martelli, C. Morandi, and M. Vascotto, “Compensation of random eye motion in television opthalmoscopy : preliminary results,” IEEE Trans: Med. Imaging, vol. MI-6, pp. 74- 81, 1987. S . Alliney and C. Morandi, “Digital image registration using projections,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 222-233. 1986.

vol. 7 , pp. 180-188, 1984.

UK: IFS(Pub1ication) Ltd., 1985, pp. 229-233.

[ l8] E. De Castro and C. Morandi, “Registration of translated rotated images using finite Fourier transforms,” IEEE Trans. Pattern Anal. Ma- chine Intell., vol. PAMI-9, pp, 700-703, 1987.

[I91 R. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. ZEEE, vol. 66, pp. 51-83, 1978.

[20] H . H. Barrett and W. Swindell, Radiological Imaging The Theory of Image Formation, Detection and Processing, Vols. I and 11. New York: Academic, 1981.

[21] D-J. Lee, T. F. Krille, and S . Mitra, “Power cepstrum and spectrum techniques applied to image registration,” Appl. Opt., vol. 27, pp. 1099-1106, 1988.

[22] J . H. Bursch, H. J. Hahne, R. Brennecke, D. Gronemeier, and P. H. Heintzen, “Assessment of arterial blood flow measurements by digital angiography,” Radiol., vol. 141, pp. 39-47, 1981.

[23] R. A. Kruger, W. Bateman, P. Y. Liu, and J . A. Nelson, “Blood flow determination using recursive processing: a digital radiographic method,” Radiol., vol. 149, pp. 293-298, 1983.

[24] R. A. Kruger, “Estimation of the diameter of and iodine concentration within blood vessels using digital radiography devices,” Med. Phvs.. vol. 8. DD. 652-658. 1981. nificantly reduced [24]. I I .

translational motion compensation for coronary angiogram sequences

Documents