(NASA-CR-197032) SSME PROPELLANT N95-16029 PATH LEAK DETECTION REAL-TIME Final Report, 20 Nov. 1989 - 31Jul. 1994 (Tennessee Univ.) 54 p Uncl as G3/28 0030180 NASA-CR-197032 f FINAL REPORT =,of8 _ for grant titled: SSME Propellant Path Leak Detection Real-Time NAG8-140 RESEARCH SPONSORED by: George C. Marshall Space Flight Center Marshall Space Flight Center, AL 35812 NASA Technical Officer: William T. Powers, Code EB22 Principal Investigators: Dr. R. A. Crawford and Dr. L. M. Smith University of Tennessee Center for Space Transportation and Applied Research UTSI Research Park Tullahoma, TN 37388-8897 Period: November 20, 1989 through July 31, 1994 Final Technical Report for NAG8-140 SSME Propellant Path Leak Detection Real-Time PIs: R. A. Crawford and L. M. Smith The fonowing four documents outline the technical aspects of the research performed on NASA Grant NAG8-140 and, while separate, should provide a complete description of the work performed during the active period November 20, 1989 to July 31, 1994. The corresponding period of work effort and references for each paper are as follows: . November 10, 1989 to June 30, 1991: J. A. Malone and L. M. Smith, "A System for Sequential Step Detection with Appli- cation to Video Image Processing," IEEE Transactions on Industrial Electronics, vol. 39, pp. 277-284, published August 1992. 4 July 1, 1991 to June 30, 1992: J. A. Malone, L. M. Smith and R. A. Crawford, "Leak Detection from the SSME Using Sequential Image Processing," Proceedings of the Advanced Earth._o- Orbi_ Propulsion Technology Conference 1992, NASA CP-3174, pp. 180-189, published June 1992. . July 1, 1992 to July 31, 1992 (and prior effort): L. M. Smith and B. W. Born,r, "Digital Image Processor Specifications for Real-Time w SSME Leak Detection," Contract Report, published July 1992. July 31, 1992 to May 31, 1994: o W. A. Hunt and L. M. Smith, "A Color Change Detection System for Video Signals with Applications to Spectral Analysis of Rocket Engine Plumes," Proceedings of the Advanced Ear,h-to-Orbit Propulsion Technology Conference 199_, to be published. Further information regarding peripheral aspects of this work can be found in the following student theses and dissertations (not included): lo A. A. Shohadaee, "Leak Detection Feasibility Investigation Using Infrared Radiation Transfer in Absorbing, Emitting and Scattering Media," Doctoral Dissertation, De- partment of Mechanical Engineering, The University of Tennessee, Knoxville, TN, 1990. ° J. A. Malone, "A System for Leak Detection Using Sequential Image Processing," Master's Thesis, Department of Electrical Engineering, The University of Tennessee, Knoxville, TN, 1991. ° W. A. Hunt, "A System for the Detection of Color Changes Using Sequential Image Processing," Master's Thesis, Department of Electrical Engineering, The University of Tennessee, Knoxville, TN, 1994. IEEE TRANSACTIONS ON INDUSTRIAl. ELEC-_'RONICS, VOL. 3q, NO. 4, AUGUST 1992 277 PAGE IILANK NOT FILMED A System for. Sequential Step Detection with Application to Video Image Processing I Jo Anne Malone, Member, IEEE, and L. Montgomery Smith, Member, IEEE T Abstra_--A method fordetecting the occurrenceofan abrupt Sequential image processing methods for detecting steplikechangeina time sequence ofvideo imagesIspresented. changes in dynamic scene analysis that have been previ- A single-pole recursive high-pass filter cascaded with a moving ously implemented are predominately used for monitoring average filter processes the Input data to remove the quiescent land resources. Although these methods are effective for background level and accumulate a sustained change In ampli- tude. The absolute value of the output is compared to a thresh- the purposes for which they were designed, they are not old to decide whether a steplike change In signal amplitude has particularly applicable to detecting steplike changes. For occurred. It is shown that, for a given cutoff frequency of the example, many land-use techniques employ various forms high-pass filter,an optimalvalueexists forthe number ofterms of temporal differencing [1]-[5]. Other algorithms use in themovingaverage.Considerations forimplementationofthe algorithm on practical image processors are discussed. The threshoiding [3]or detect changes by image ratioing where results of numerical and laboratory experiments are presented the ratio of the previous image to the current image is thatverifythe effectiveness of the method. found and the difference from unity of the ratio indicates a change has occurred [3]. Since these schemes are used to detect changes that occur slowly over time, only the I. INTRODUCTION present image and a few previous images are used. The limited number of sample values makes these systems N dynamic monitoring of a sequence of images, the unsuitable for steplike change detection, since the sus- detection of a sudden but sustained change is often a tained nature of the change is not exploited. desired objective. The application giving rise to the method Another somewhat related application istarget tracking presented in this paper is the detection of high-pressure systems that use image sequences to detect and follow the gas leaks using infrared and visible imaging. However, the presence of targets or objects [6]-[8]. The techniques used same objective applies to any situation in which the inten- sity at one spatial location in a time sequence of images include spatial differencing combined with temporal dif- ferencing, as well as algorithms using matched filters and abruptly changes from its quiescent value to something different. Thus, a motivation exists for developing a sys- peak detection [6]. Furthermore, the system in [7] and [8] tem that can quickly and automatically detect a steplike determines the trajectory of targets using dynamic pro- change in intensity occurring within a given field of view gramming, Although these techniques monitor changes in of an image. Because of the likely possibility of extrane- image sequences, their objective is markedly different ous intensity fluctuations, the system should also be ro- than detecting a steplike change in intensity. For this bust with respect to the noise corrupting the signal. The reason, they are not readily extended to the application considered here. problem is that of detecting a step function in the pres- ence of noise. Among one-dimensional analyses, detection of abrupt Time-varying intensity values within a video image con- steplike changes has been studied as an edge detection problem for jumps occurring spatially within an image stitute an inherently discrete signal with a sampling rate [9]-[11]. A noteworthy approach taken by Basseville, of 30 Hz for standard television format. Thus, techniques Espiau, and Gasnier, [10], [11], considers each line of the of digital signal processing are directly applicable to this analysis. Earlier research in digital signal processing has image to be a sequence of independent Gaussian random considered similar problems to that addressed in this variables having the same variance. An edge is defined as a jump in the mean value of the sequence and is detected study, but with marked differences in approach and appli- cability. This previous work roughly falls into two cate- using Hinckley's algorithm. Hinckley's algorithm, as de- gories: multidimensional methods involving sequential im- scribed by Basseville [11], computes the cumulative sum of age processing and one-dimensional methods. the sequence and the maximum of the sum to detect positive jumps. A second detector is required for negative jumps. Despite their effectiveness, these spatial processing Manuscript received July 9, 1991; revised February 15, 1992. This work methods are inherently noncausal. Therefore, they also was supported by the National Aeronautics and Space Administration and the Center for Space Transportation and Applied Research under are not readily extendable to sequential image processing. grant NAG8-140. In addition to the edge-detection schemes, one-dimen- The authors are with the Center for Laser Applications, University of sional algorithms have been developed for detecting Tennessee Space Institute, Tullahoma, TN 37388-8897. IEEE Log Number 9201270. abrupt changes in discrete-time sequences such as speech, 0278-0046/92503.00 © 1992IEEE 27/4 II'_EE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 39, NO. 4, AUGUST 1992 electrocardiogram, and geophysical signals [12]-[15]. to be passed. The output of the high-pass filter is next However, these techniques are usually tailored to detect input to a moving average filter, which sums over the changes in the overall spectral characteristics of the signal present and previous J sample values. Thus, only a change and not a specific signal artifact, such as a step function. that is maintained will cause a substantial change in the The method presented in this paper is an efficient average. The absolute value block creates a positive value causal algorithm for detecting an abrupt steplike change in case the change was negative, and the result is com- w in intensity in sequential video images. A reeursive digital pared to a threshold to decide if a step has occurred. An high-pass filter is used to remove slowly varying quiescent entire image isanalyzed by implementing the algorithm at intensity levels without the need to compute a mean value every point in the image. estimate. This filter is cascaded with a moving average The following discussion describes the step detection filter that accumulates a sustained change in amplitude. algorithm in detail. To simplify notation, all signals are The number of terms in the moving average is chosen to written simply as functions of the time variable index n. maximize the signal-to-noise ratio for a given high-pass For video images, all signals depend on two spatial posi- filter cutoff frequency. The absolute value of the output of tion coordinates in addition to the time variable. How- the moving average iscompared with a threshold to detect ever, because processing is carded out only with respect the occurrence of either positive or negative jumps. The to the time index, the spatial dependence is suppressed in threshold used in this method is a function of the input the notation. noise variance and the number of terms in the moving For computational efficiency and rapid response, the average and provides explicit control over the probability high-pass filter was chosen to be a single-pole unity-gain of false detections. This algorithm has been implemented recursive digital filter with a z-domain transfer function both in floating-point arithmetic on a digital computer for given by simulation studies and in fixed-point arithmetic on a digi- tal image processor for practical application to video data. i It has been found to be computationally efficient and H(z) = 1+/23( I"l--z=-1_--_I ) • (I) effective for detecting sudden but sustained changes. Al- _,_:_. though implementation to date has not realized real-time This expression was obtained by applying the bilinear processing, currently available image processing hardware transformation [16, pp. 608--612] to a single-pole continu- utilizing full-frame arithmetic logic units (ALU's) should ous transfer function of the form s/(s + fZc). The dis- allow video signal processing at standard framing rates. crete cutoff frequency of the filter is set by choice of the Section II describes the step detection algorithm. The pole value/3. The relationship between 13and the -3 db optimal choices for the parameters of the high-pass filter normalized discrete cutoff frequency (oc is found by mak- and moving average will be derived. Some of the consider- ing the substitution z--e i" in (1) and solving for the ations involved in the practical implementation of the value of w at which the magnitude of the transfer func- algorithm on digital image processors are discussed in tion IH(ei")l equals 1/)/2. Explicitly, these parameters Section III. The algorithm has been tested in a numerical are related by study using simulated data and has been implemented on 1 - sin toc 1 -/3 an image processing system. The procedures and results /3= toc -- 2sin- i (2) of these tests will be presented in Section IV. Summary cos _,_ _2(1 +/32) and conclusions are given in Section V. ,,-4. Note that the use of a recursive or infinite impulse re- i II. THE STEPDETECTIONALGORrrHM sponse (IIR) filter utilizes all of the past information in The overall goal of the step detection system is to the input signal. provide binary step/no-step occurrence decisions at the If the output of the high-pass filter is denoted by x(n), input data sampling rate. In addition, the following prop- the moving average computes its output as erties are highly desirable: 11-I 1) The algorithm should be computationally efficient y(n) = --j __,x(n - k). (3) k-O for real-time processing of video data. 2) It should be impervious both to different back- The magnitudes of the sample values of y(n) are then ground or quiescent intensity levels at separate loca- compared to a preset threshold value T and if [y(n)l > T, tions within the image and to signal noise. the decision is made that a step has occurred. Otherwise, 3) It should be capable of detecting steps over a wide it isdecided that no step has occurred. range of amplitudes, both positive and negative. It will be shown that for a given high-pass filter cutoff frequency (o_with corresponding pole value/3, an optimal i The system developed to achieve these objectives is choice exists for the number of terms J in the moving shown in Fig. 1. The input data is first filtered with a average. To derive this, an input signal of the form high-pass filter to remove the slowly or nonvarying back- ground intensity level while allowing any sudden changes w(n) = b(n) + Au(n) + e(n) (4:) MALONE AND SMITIt: A SYSTEM FOR SEQUENTIAL STEP DETECTION 279 "" I rL- 'l I v'l Thruhotd Fig. 1. Block diagram of the step detection system. t is assumed where b(n) represents a slowly varying back- In practice, J ischosen to the nearest integer to the value ground intensity level, u(n) is a unit step function, A the computed in (10). Thus, from a given cutoff frequency amplitude of the step, and ¢(n) is a zero-mean white chosen to remove the background component from the random sequence representing the noise. If it is assumed signal, the high-pass filter pole value/3 is calculated from that the high-pass filter removes the background com- (2), and a value for the moving average summation J is pletely, then from the transfer function given in (1), its chosen from (10) to maximize the signal-to-noise ratio of output can be shown to be the filtered sequence. As a final comment, note that in the absence of noise, a x(n) = ½A(1 + fl)fl"u(n) + h(n)* _(n) (5) step will be detected provided that its amplitude is suffi- where h(n) is the impulse response of the filter in (1) and ciently large such that the magnitude of the signal term in the asterisk (.) denotes convolution. In practical applica- (7) exceeds the threshold value. That is, with no noise tions, the cutoff frequency of the high-pass filter is usually corrupting the signal, a step must have an amplitude low. Thus, its effect on the spectral and statistical proper- satisfying ties of the white noise sequence ¢(n) is small. With the assumption that this effect isnegligible, to a close approx- imation, the sequence x(n) can be written IAI> 1-_J _ (11) x(n) "- ½A(1 + fl)fl"u(n) + e(n). (6) to be detected. This expression provides a lower limit of The moving average filter sums the previous J values of detection that isuseful in evaluating the statistical perfor- this sequence. The maximum amplitude of the signal mance of the step detection algorithm as in the numerical resulting from the step function occurs J- 1 samples study presented in Section IV. later. At that instant, y(J - 1) is given by III. IMPLEMENTATION CONSIDERATIONS The system on which this algorithm was implemented Y(:-1)=iA7(1+/3) (I-/3'+)71k1-E10'(n-k) for image processing in this study was a i386-based per- (7)sonal computer with a CPU speed of 25 MHz. A DT-2861 frame grabber card and a DT-2858 auxiliary frame proces- The standarddeviatioonftheJ-pointaverageof e(n- sor card manufactured by Data Translation were installed k)isgivenby_r/77,wherecristhestandarddeviatioonf in the unit and used for image data acquisition, process- thewhitenoisesequence_(n).Thus,a signal-to-noisineg, and display. Several aspects of the step detection ratioforthissystemcan be definedastheratioof the algorithm require special consideration when it is imple- magnitudeofthemaximum signalstepresponse(thefirstmented on such practical digital image processing systems. termon theright-hansdideof(7))tothestandarddevia- One consideration involves the arithmetic operations real- tionoftheprocessednoisesignal: izing the filters. Others are concerned with minimizing the effects of finite precision fixed-point arithmetic in the filtering operations and avoiding false detections due to transients at start-up. Also, the threshold value must be chosen to reduce false detections due to noise while This signal-to-noise ratio, considered to be a function of maintaining a suitable level of sensitivity. This section J, can be maximized in the following manner. Differentia- discusses these considerations and presents some methods tion of this expression with respect to J and setting the that have been employed to reduce adverse effects. result to zero yields the optimal value as the solution to Because each sequence value processed in the step the transcendental equation detection algorithm actually represents one element of a two-dimensional image array with many elements, arith- /3J(1 - 2In/3 J) = I (9) metic operations in the filter implementation involve a which can be solved numerically to yield large amount of computation. However, frame processor 1.2564 ALU's can quickly perform addition of image frames. J = (10) Furthermore, the point-by-point multiplication of array in/3 element values can be carried out by noting that frame 280 IEEE TRANSA(.'I'ION5 ON INDUS 11_IAL ELI_C'I'kUNIC_,, VUL. J'_, NO. 4, AU_JUb 1 I'-I".I--" buffers in digital image processors are usually configured of a random sequence with standard deviation _r/vrj. If it for fixed-point or integer pixel values (typically 8 b). Thus, is further assumed that this random signal is Gaussian only a finite number of products exist for any multiplica- distributed, the probability of a false detection (i.e., that tion by a constant-valued filter coefficient. Multiplications the magnitude of the processed noise exceeds the thresh- are thus realized via look-up-tables (LUT's) with precom- old) at each sample instant will be 2 x 10-4 for a thresh- puted values for each possible product. old value of By realizing the coefficient multiplications via LUT's, 3.70tr and utilizing the ALU for additions, each add/multiply T= ¢7 (15) computation pair requires approximately 300 ns per pixel according to the manufacturer's specifications. This exe- F Other false detection probabilities can be realized by cution time can be compared to that of the host processor choosing other constants of proportionality in accordance by assuming that each add/multiply pair in the sum of with tabulated Gaussian probabilities [18].The value given products consists of a minimum of two data movements, in (15) has been found to provide acceptable performance one integer multiply, one arithmetic shift, one integer for practical applications. add, and one loop instruction. This amounts to approxi- mately 46 clock cycles, which, for a CPU speed of 25 IV. NUMERICAL AND EXPERIMENTAL RESULTS MHz, corresponds to 1.84 p.s execution time. Thus, a To evaluate the statistical performance of the step sixfold increase in computation time is a conservative detection algorithm, a numerical study was conducted by estimate of the advantages of this technique. first implementing the algorithm in a FORTRAN program Implementation of the recursive high-pass filter can be as follows. Tests were conducted by processing 256-point accomplished with minimal storage requirements and with data blocks where the time variable index n ranged from reasonable computational efficiency by using a state-space 0 to 255. For each n, the value of the input w(n) as given filter structure. The output x(n) is computed from the by (4) was generated with b(n) an arbitrary constant. The input w(n) and a state variable u(n) by means of the step occurred at some random time to, uniformly dis- following two equations tributed over the 256-point data block. The additive noise .,= v(n + 1) - ao(n) + bw(n) was an uncorrelated Gaussian random sequence gener- (12) w ated by [16, pp. 132-133] x(n) = cu(n) + dw(n) where a, b, c and d are constant-valued coefficients e(n) -- o'v/-21n ul(n ) eos[2cru2(n)] (16) chosen to realize the transfer function of (1). Specifically, where ul(n) and u2(n) were random numbers uniformly these coefficients must satisfy distributed on (0, 1) generated from an intrinsic function bcz-_ within the program. The state-space filter structure in(12) = = H(z) = 1 - az-1 + d. (13) was used to remove the background intensity and update the state variable for the next input value. The moving This determines the values for a and d as a --/3, and average was used next to average the present value of the d = ½(1+/3). high-pass filter output x(n) with the previous J - 1terms Because of the fixed-point or integer format of the of x(n) where x(n) = 0 for n < 0. The output of the two-dimensional array element values, overflow in the moving average y(n) was then compared to the threshold. state variable computation must be eliminated. This is If ly(n)l > T and n > t0, the program indicated that the accomplished by using L®-norm scaling [17], which, for a step was correctly detected. Otherwise, if ly(n)l exceeded stable first-order filter with positive pole value, ensures the threshold while n < t0,or if ly(n)[ failed to exceed the that the magnitude of the state variable never exceeds threshold at any time during the 256-point data block, the that of the input. This sets the values for b and c as program indicated that the algorithm failed to detect the b-_l-/3, andc--- ½(1+/3). step correctly. The procedure was repeated for each value To avoid transients in filtered data at start-up, the state of n until either a step was detected or n > 255. variable is initialized to produce zero output for the first To obtain a measure of the performance of the algo- sample. This is accomplished by using the first input rithm, the foregoing process was performed many times sample to compute its initial value by for step amplitudes ranging from 0 to 155 and varying d times of occurrence. The algorithm was tested with 100 v(O) = --w(O) = w(0). (14) different input sequences each having the same step am- c plitude but different times of occurrence and with a Because the step amplitude is not known a priori, the different sequence of additive noise. Each time the algo- threshold value must be chosen to reduce the probability rithm correctly detected the step, a counter was incre- -of a false detection to an acceptable level. If the effect of mented. The number of correct detections out of the 100 the high-pass filter on the input noise is assumed negligi- trials was recorded for the step size used and the process ble as discussed in the previous section, then the pro- was repeated for all step sizes. The number of correct cessed data in the absence of a step input consists s!mply detections for each step size was converted to an esti- p O QInAL PA oFI :m Qu ¢tv MALONE AND SMITH: A SYSTEM FOR SEQUENTIAL STEP DETECTION 281 |.o_ ;.O F ,"F- 0.0 -- i pr 0"8 t Pr" o o T b 0.8 b I T '1 !i b•°I]0.6_ I; ¥ y o.,! K,/II, I l _ i I I I i i . tl. ;"I l t _al i .ii'i, i II.T,,T=_; _-i!i I i i I I[ ,, ; 0.0 ,,i. i i_' ..r. 0 2';' _0 ?_ 100 '.25 150 175 0 25 SO 7S :00 *-2_. 1.50 17.5 1 Step Size SLCO Size (b) (a) L_ . = T :.0 w ,..¢I., P P 0 1;)O.S- T a 0 1 I I 0._, "r Y _ 1 0.2 7 i i *, I ! l _ , I 0.0 0.0 ....:i .... ;;....II .....;......, ., Ii:''_I 0 _.5 '_0 7'5 ",00 '-25 :'_0 17_ Step .qlze 5te= S;ze (c) (d) Fig. 2. Results of numerical evaluation of the step detection algorithm. These plots show the calculated probability of correct detection versus step amplitude for processing 256-point input data blocks corrupted by noise with standard deviations of (a) 10, (b) 20, (c) 30, and (d) 40. mated probability and plotted as a function of the step of noise in the input is overestimated, as in plot (a), the size. The input noise variance was held constant for a detector is very accurate for large step sizes and the given series of trials. minimum step size detected is close to the value 55.4 Fig. 2 shows representative results of performing these given by (11) for this example. Plot (b) demonstrates the tests with /3-- 0.7951, J = 5, and the threshold fixed at performance of the algorithm for the threshold criterion T = 33.1. This value of/3 was chosen somewhat arbitrar- described in Section III where the assumed noise stan- ily for a cutoff frequency slightly more than 1 Hz in a dard deviation exactly matches that of the noise actually 30-Hz sampling rate system. The threshold corresponds to in the input. As the standard deviation of the input noise using the criterion in (15) with an assumed input noise is increased, as shown in plots (c) and (d), the algorithm standard deviation of o"= 20. Shown are four plots of becomes less effective. Although smaller steps are de- probability of correct detection versus step amplitude for tected more frequently, the increase is due to serendipi- actual input noise standard deviations of 10, 20, 30, and tous effects of noise causing the processed signal magni- 40. tude to exceed the threshold after the occurrence of the This series of plots illustrates the relationship between step. The noise also causes false detections prior to the the standard deviation of the input noise and the assumed occurrence of the step, which results in decreased perfor- standard deviation used to set the threshold. If the level mance for large step amplitudes. Note that once the 282 lli[_l_ "II_.AN++++;A(TI'IONS ()N INL)USTF.IAI. I_I.I'X-I F.ONI('N, V,()I+. 39, N(J ,I, AtJ(+IUS i i_92 standard deviation of the noise on the input becomes twice as large as the standard deviation used to set the threshold (plot (d)), the probability of detecting any step correctly is effectively that of guesswork. Therefore, a noteworthy property is that although overestimating the standard deviation of the noise (Fig. 2(a)) reduces sensitiv- ity in terms of the minimum detectable step amplitude, the performance of the algorithm isotherwise not severely affected as it is inthe ease where the standard deviation is L underestimated (Figs. 2(c), (d)). As the tests described above demonstrate, the perfor- mance of the algorithm is affected by the magnitude of L the step and the amount of input noise. However, param- eters of the data that do not affect performance are the background value and the direction (positive or negative) _ _+ = of the step. As shown by the transfer function (1), the (a) high-pass filter assures that any constant background in- tensity value is removed before processing the data block. The sign of the step isirrelevant since the absolute value of the average is taken before comparing it to the thresh- old. An experimental study was performed by implementing and testing the algorithm on the digital image processor using the techniques discussed in Section III. Image data were acquired from RS-170 standard video format signals and stored in 512 x 512 pixel format with 8 b per pixel. The detection program written for this experiment al- lowed interactive processing of selected input frames as follows. Live video was shown on the display monitor of the image processor until the operator initiated acquisi- tion of one frame of the incoming signal. This frame was input to the detection algorithm and processed. The out- 0:0 put of the algorithm was then displayed as a binary image. Fig.3. Photographsoftheinputvideoimagesusedintheexperimental w At any location where a steplike change was detected the testingof the step detection algorithm.(a) Referencetest scene.(b) Alteredscene. pixel was set white; locations where no change was de- E__ tected were displayed as black. Once the indication was made to continue, live video was again shown on the However, it should be noted that real-time video signals display monitor, and the process repeated. For the experi- including noise were acquired and processed to obtain ment, a camera was connected to the image processor for these images. Because the algorithm is designed to detect acquiring live video of a laboratory scene. A reference test a sustained change, the white areas indicating detected scene was set up and several frames of this image were change do not immediately appear. Instead, they grow processed. The scene was subsequently altered and pro- from one output image to the next and reach a maximum cessing continued. in the fifth frame processed after the scene was altered Figs. 3 and 4 are photographs taken during the experi- (Fig. 4(e)). They then shrink over Fig. 4(0-(h) since the ment. For this experiment, the same values /3= 0.7951 altered image itself is not changing and the transient and J ,_ 5 were used as in the preceding numerical study. response of the filters is decaying. Because the noise contributed by the camera and lighting Processing time for the algorithm is obviously depen- variations was assumed to be low, the threshold was set dent on the number of pixels in the images and the using (15) for an input noise standard deviation of 5,0 gray number of terms in the moving average. For the system levels. (The 8-b input pixel intensity values ranged from 0 used in this study with the parameters as given in the to 255.) Fig. 3(a) shows the reference test scene. As preceding example, execution time was approximately 1.12 i expected, no detected changes were indicated in the bi- s per frame. Although this exceeds the _-s time required nary output image during processing of this image. The for real-time processing of video signals, the relatively altered scene isshown in Fig. 3(b). Fig. 4(a)-(h) shows the inexpensive and general-purpose nature of the hardware locations where changes were detected as the sequence of used should be considered. Also, programming was car- images of the altered scene was processed. Because the ried out in a higher level language (FORTRAN) utilizing scene was altered only once, the input frames for Fig. a subroutine library supplied by the manufacturer. It 4(a)-(h) appear identical to Fig. 3(b) and are not shown. seems reasonable to conclude that real-time implementa- B 4 MALONE AND SMI'I] l: A SYSTEM FOR SEQUENTIAl. STEP DETECTION 283 ,'7" "t Co) (a) - ? (c) (d) I (e) (0 E _) (h) Fig. 4. Sequence of binary output images obtained by processing video images of the altered .scene in Fig. 3(b) with the step detection algorithm. White areas represent locations of detected change. tion of this method is feasible with present technology, mented, and tested. The detection algorithm presented provided that more expensive or special-purpose hard- functions by filtering the input data to remove the quies- ware is utilized and programming is carried out in mi- cent background intensity and comparing the output of a crocode or assembly language. moving average to a threshold. When the average exceeds the threshold, a step has been detected. This method is V. SUMMARY AND CONCLUSIONS computationally efficient and isapplicable to implementa- A method for detecting abrupt, steplike changes in a tion on digital image processors using fixed-point or inte- time sequence of images has been developed, imple- ger arithmetic. ii