(1984)Pyramid Methods in Image Processing

Pyramid methods in image processing

The image pyramid offers a flexible, convenient multiresolutionformat that mirrors the multiple scales of processing in thehuman visual system.Digital image processing is being used in

many domains today. In image enhance-ment, for example, a variety of methodsnow exist for removing image degrada-tions and emphasizing important image in-formation, and in computer graphics, dig-ital images can be generated, modified, andcombined for a wide variety of visualeffects. In data compression, images may beefficiently stored and transmitted if trans-lated into a compact digital code. In ma-chine vision, automatic inspection systemsand robots can make simple decisions basedon the digitized input from a televisioncamera.

But digital image processing is still in adeveloping state. In all of the areas justmentioned, many important problems re-main to be solved. Perhaps this is mostobvious in the case of machine vision: westill do not know how to build machinesAbstract: The data structure used to

represent image information can be criticalto the successful completion of an imageprocessing task. One structure that has

attracted considerable attention is the imagepyramid This consists of a set of lowpass orbandpass copies of an image, eachrepresenting pattern information of a

different scale. Here we describe a variety ofpyramid methods that we have developedfor image data compression, enhancement,analysis and graphics.

©1984 RCA Corporation

Final manuscript received November 12, 1984Reprint Re-29-6-5

RCA Engineer • 29-6 • Nov/Dec 1984

that can perform most of the routine vis-ual tasks that humans do effortlessly.

It is becoming increasingly clear thatthe format used to represent image datacan be as critical in image processing asthe algorithms applied to the data. A dig-ital image is initially encoded as an arrayof pixel intensities, but this raw format isnot suited to most tasks. Alternatively, animage may be represented by its Fourier

transform, with operations applied to thetransform coefficients rather than to theoriginal pixel values. This is appropriatefor some data compression and image en-hancement tasks, but inappropriate forothers. The transform representation is par-ticularly unsuited for machine vision andcomputer graphics, where the spatial loca-tion of pattem elements is critical.

Recently there has been a great deal ofinterest in representations that retain spa-tial localization as well as localization in

the spatial—frequency domain. This isachieved by decomposing the image into aset of spatial frequency bandpass compo-nent images. Individual samples of a com-ponent image represent image pattern in-formation that is appropriately localized,while the bandpassed image as a whole rep-resents information about a particular fine-ness of detail or scale. There is evidencethat the human visual system uses such arepresentation,1 and multiresolution sche-mes are becoming increasingly popular inmachine vision and in image processing ingeneral.

The importance of analyzing images atmany scales arises from the nature ofimages themselves. Scenes in the world

contain objects of many sizes, and theseobjects contain features of many sizes.Moreover, objects can be at various dis-tances from the viewer. As a result, anyanalysis procedure that is applied only at asingle scale may miss information at otherscales. The solution is to carry out analy-ses at all scales simultaneously.

Convolution is the basic operation ofmost image analysis systems, and convo-lution with large weighting functions is anotoriously expensive computation. In amultiresolution system one wishes to per-form convolutions with kernels of manysizes, ranging from very small to verylarge. and the computational problemsappear forbidding. Therefore one of the

main problems in working with multires-olution representations is to develop fastand efficient techniques.

Members of the Advanced Image Pro-cessing Research Group have been activelyinvolved in the development of multireso-lution techniques for some time. Most ofthe work revolves around a representationknown as a \"pyramid,\" which is versatile,convenient, and efficient to use. We haveapplied pyramid-based methods to somefundamental problems in image analysis,data compression, and image manipulation.Image pyramids

The

task of detecting a target pattern thatmay appear at any scale can be approachedin several ways. Two of these, which in-volve only simple convolutions, are illus- 33

Fig. 1. Two methods of searching for a target pattern overmany scales. In the first approach, (a), copies of the targetpattern are constructed at several expanded scales, andeach is convolved with the original image. In the secondapproach, (b), a single copy of the target is convolved withcopies of the image reduced in scale. The target should bejust large enough to resolve critical details The two ap-proaches should give equivalent results, but the second ismore efficient by the fourth power of the scale factor (imageconvolutions are represented by 'O').

trated in Fig. 1. Several copies of the pat-tern can be constructed at increasing scales,then each is convolved with the image.Alternatively, a pattern of fixed size can beconvolved with several copies of the imagerepresented at correspondingly reduced re-solutions. The two approaches yield equi-valent results, provided critical informationin the target pattern is adequately repre-sented. However, the second approach ismuch more efficient: a given convolutionwith the target pattern expanded in scale by a factor s will require s4 more arith- metic operations than the corresponding

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convolution with the image reduced inscale by a factor of s. This can be substan-tial for scale factors in the range 2 to 32, acommonly used range in image analysis.The image pyramid is a data structuredesigned to support efficient scaled convo-lution through reduced image representa-tion. It consists of a sequence of copies ofan original image in which both sampledensity and resolution are decreased inregular steps. An example is shown in Fig.2a. These reduced resolution levels of thepyramid are themselves obtained through ahighly efficient iterative algorithm. The

bottom, or zero level of the pyramid, G0, is equal to the original image. This is low-pass-filtered and subsampled by a factor oftwo to obtain the next pyramid level, G1.G1 is then filtered in the same way andsubsampled to obtain G2. Further repeti-tions of the filter/subsample steps generatethe remaining pyramid levels. To be pre-cise, the levels of the pyramid are obtainediteratively as follows. For 0 < l < N:

(1)Gl (i,j) ΣΣ w (m,n) Gl-1 (2i+m,2j+n)

mn

However, it is convenient to refer to this

RCA Engineer • 29-6 • Nov/Dec 1984

Fig. 2b. Levels of the Gaussian pyramid expanded to the size of the original image.The effects of lowpass filtering are now clearly apparent.reduced correspondingly by one octave witheach level. Because of this resemblance tothe Gaussian density function we refer tothe pyramid of lowpass images as the\"Gaussian pyramid.\"Bandpass, rather than lowpass, imagesare required for many purposes. These maybe obtained by subtracting each Gaussian(lowpass) pyramid level from the next-lower level in the pyramid. Because theselevels differ in their sample density it isnecessary to interpolate new sample valuesFig.3. Equivalent weighting functions.between those in a given level before thatThe process of constructing the Gaus-level is subtracted from the next-lowersian (lowpass) pyramid is equivalent tolevel. Interpolation can be achieved byconvolving the original image with a set reversing the REDUCE process. We callof Gaussian-like weighting functions,this an EXPAND operation. Let Gl,k bethen subsampling, as shown in (a). Thethe image obtained by expanding Gl kweighting functions double in size withtimes. Then Gl,k = EXPAND [G Gl,k-1] or, to beeach increase in 1. The correspondingprecise, Gl,0 = Gl, and for k>0,functions for the Laplacian pyramid re-(2)semble the difference of two Gaussians,G2i+mas shown in (b).l,k(i,j) = 4 ΣΣGl,k-1 ( ,2j+nmn22 )

process as a standard REDUCE opera- Here only terms for which (2i+m)/2 and

tion, and simply write

(2j+n)/2 are integers contribute to theGsum. The expand operation doubles thel = REDUCE [Gl-1].We call the weighting function w(m,n)size of the image with each iteration, so

the \"generating kernel.\" For reasons ofthat Gl,1, is the size of Gl,1, and Gl,1 is the

computational efficiency this should besame size as that of the original image.

small and separable. A five-tap filter wasExamples of expanded Gaussian pyramid

used to generate the pyramid in Fig. 2a.levels are shown in Fig. 2b.

Pyramid construction is equivalent toThe levels of the bandpass pyramid, L0,

convolving the original image with a set ofL1, ...., LN, may now be specified in terms

Gaussian-like weighting functions. These

of the lowpass pyramid levels as follows:

\"equivalent weighting functions\" for three

Ll = Gl—EXPAND [Gl+1] (3)successive pyramid levels are shown in Fig. 3a. Note that the functions double in

= Gl—Gl+1,1.

width with each level. The convolution

The first four levels are shown in Fig. 4a.acts as a lowpass filter with the band limit

Just as the value of each node in theAdelson et al.: Pyramid methods in image processing

Gaussian pyramid could have been ob-tained directly by convolving a Gaussian-like equivalent weighting function with theoriginal image, each value of this bandpasspyramid could be obtained by convolvinga difference of two Gaussians with theoriginal image. These functions closelyresemble the Laplacian operators common-ly used in image processing (Fig. 3b). Forthis reason we refer to the bandpass pyra-mid as a \"Laplacian pyramid.\"An important property of the Laplacianpyramid is that it is a complete image

representation: the steps used to constructthe pyramid may be reversed to recoverthe original image exactly. The top pyra-mid level, LN

, is first expanded and addedto LN-1 to form GN-1 then this array isexpanded and added to LN-2 to recoverGN-2, and so on. Alternatively, we maywriteG0 = ∑ Ll,l (4)The pyramid has been introduced here asa data structure for supporting scaled image

analysis. The same structure is well suitedfor a variety of other image processing

tasks. Applications in data compressionand graphics, as well as in image analysis,will be described in the following sections.It can be shown that the pyramid-buildingprocedures described here have significantadvantages over other approaches to scaledanalysis in terms of both computation costand complexity. The pyramid levels areobtained with fewer steps through repeatedREDUCE and EXPAND operations than ispossible with the standard FFT. Further-more, direct convolution with large equiva-lent weighting functions requires 20- to30-bit arithmetic to maintain the same ac- 35

Fig. 4b. Levels of the Laplacian pyramid expanded to the size of the original image.Note that edge and bar features are enhanced and segregated by size.image can be exactly reconstructed from it'spyramid representation (Eq. 4), the pyramidcode is complete.

There are two reasons for transforming an image from one representation to an-A compact codeother: the transformation may isolate criti-The Laplacian pyramid has been described ascal components of the image pattern so a data structure composed of bandpassthey are more directly accessible to analy-sis, or the transformation may place the copies of an image that is well suited

for scaled-image analysis. But the pyramiddata in a more compact form so that they may also be viewed as an image transform-can be stored and transmitted more effi-ation, or code. The pyramid nodes are thenciently. The Laplacian pyramid serves bothconsidered code elements, and the equiva-of these objectives. As a bandpass filter,lent weighting functions are samplingpyramid construction tends to enhancefunctions that give node values when con-image features, such as edges, which arevolved with the image. Since the originalimportant for interpretation. These featurescuracy as the cascade of convolutions withthe small generating kernel using just 8-bitarithmetic.

36

are segregated by scale in the various pyra-mid levels, as shown in Fig. 4. As with theFourier transform, pyramid code elementsrepresent pattern components that are res-tricted in the spatial-frequency domain. Butunlike the Fourier transform, pyramid codeelements are also restricted to local regionsin the spatial domain. Spatial as well asspatial-frequency localization can be criticalin the analysis of images that containmultiple objects so that code elements willtend to represent characteristics of singleobjects rather than confound the characteris-tics of many objects.

The pyramid representation also permitsdata compression.3 Although it has one

RCA Engineer • 29-6 • Nov/Dec 1984

Fig. 5. Pyramid data compression. The original image represented at 8 bits per-pixel is shown in (a). The node values of tbe Laplacian pyramid representation ofthis image were quantitized to obtain effective data rates of 1 b/p and 1/2 b/p.Reconstructed images (b) and (c) show relatively little degradation.third more sample elements than the orig-These examples suggest that the pyra-cost of image processing based on such

inal image, the values of these samples mid is a particularly effective way of repre-pyramids is correspondingly increased.

A second class of operations concerns tend to be near zero, and therefore can besenting image information both for trans-represented with a small number of bits.mission and analysis. Salient informationthe estimation of integrated properties

Further data compression can be obtainedis enhanced for analysis, and to the extentwithin local image regions. For example, athrough quantization: the number of dis-that quantization does not degrade analy-texture may often be characterized by localtinct values taken by samples is reduced sis, the representation is both compact anddensity or energy measures. Reliable esti-mates of image motion also require theby binning the existing values. This resultsrobust.

integration of point estimates of displace-in some degradation when the image is

ment within regions of uniform motion. Inreconstructed, but if the quantization bins

such cases early analysis can often beare carefully chosen, the degradation willImage analysis

not be detectable by human observers andPyramid methods may be applied to anal-formulated as a three-stage sequence of

operations. First, an appropriatewill not affect the performance of analysisysis in several ways. Three of these will bestandard

algorithms.outlined here. The first concerns patternpattern is convolved with the image (orFigure 5 illustrates an application of thematching and has already been mentioned:images, in the case of motion analysis).pyramid to data compression for imageto locate a particular target pattern that This selects a particular pattern attribute totransmission. The original image is shownmay occur at any scale within an image, be examined in the remaining two stages.in Fig. 5a. A Laplacian pyramid represen-the pattern is convolved with each level ofSecond, a nonlinear intensity transforma-tation was constructed for this image, thenthe image pyramid. All levels of the pyra-tion is performed on each sample value.the values were quantized to reduce themid combined contain just one third moreOperations may include a simple thresholdeffective data rate to just one bit per pixel,nodes than there are pixels in the originalto detect the presence of the target pattern, then to one-half bit per pixel. Images recon-image. Thus the cost of searching for aa power function to be used in computingstructed from the quantized data are pattern at many scales is just one third texture energy measures, or the product of

corresponding samples in two images usedshown in Figs. 5b and 5c. Humans tend tomore than that of searching the original

in forming correlation measures for motionbe more sensitive to errors in low-frequencyimage alone.

image components than in high-frequencyThe complexity of the patterns that mayanalysis. Finally the transformed sample

are integrated within local windowscomponents. Thus in pyramid compression,be found in this way is limited by the factvalues

nodes at level zero can be quantized morethat not all image scales are represented into obtain the desired local propertycoarsely than those in higher levels. This isthe pyramid. As defined here, pyramid measures.

Pattern scale is an important parameter fortuitous for compression since three-quart-levels differ in scale by powers of two, or

ers of the pyramid samples are in the zeroby octave steps in the frequency domain.of both the convolution and integrationlevel.Power-of-two steps are adequate when thestages. Pyramid-based processing may beData compression through quantizationpatterns to be located are simple, but com-employed at each of these stages to facili-may also be important in image analysis toplex patterns require a closer match be-tate scale selection and to support efficientreduce the number of bits of precisiontween the scale of the pattern as defined incomputation. A flow diagram for this three-carried in arithmetic operations. For exam- the target array, and the scale of the pat-stage analysis is given in Fig. 6. Analysisple, in a study of pyramid-based imagetern as it appears in the image. Variants onbegins with the construction of the pyramidmotion analysis it was found that data the pyramid can easily be defined withrepresentation of the image. A feature pat-could be reduced to just three bits persquareroot-of-two and smaller steps. How-tern is then convolved with each level of thesample without noticeably degrading theever, these not on]y have more levels, butpyramid (Stage 1), and the resultingcomputed flow field.4many more samples, and the computationalcorrelation values may be passed through

Adelson et al.: Pyramid methods in image processing

37

methods have proved be useful. For ex-ample, a method we call multi-resolutioncoring may be used to reduce random noise in an image while sharpening detailsof the image itself.5 The image is firstdecomposed into its Laplacian pyramid(bandpass) representation. The samples ineach level are then passed through a cor-ing function where small values (whichinclude most of the noise) are set to zero,while larger values (which include pro-menent image features) are retained, or\"peaked.\" The final enhanced image is then obtained by summing the levels of the processed pyramid. This technique is

Fig.6. Efficient procedure for computing integrated image properties at many scales.illustrated in Fig. 8. Figure 8a is the origi-Each level of the image pyramid is convolved with a pattern to enhance an elementarynal image to which random noise has beenimage characteristic, step 1. Sample values in the filtered image may then be passedadded, and Fig. 8b shows the image en-6

through a nonlinear transformation, such as a threshold or power function, step 2.hanced through multiresolution coring.

We have recently developed a pyramid-Finally, a new \"integration\" pyramid is built on each of the processed image pyramid

levels, step 3. Node values then represent an average image characteristic integratedbased method for creating photographic

images with extended depth of field. Wewithin a Gaussian-like window.

begin with two or more images focused at

a nonlinear intensity transformation (StageNote that texture differences in the originaldifferent distances and combine them in a

that retains the sharp regions of each.2). Finally, each filtered and transformedimage have been converted into differen-way

image becomes the bottom level of a newces in gray level. Finally, a simple gra-As an example, Figs. 9a and 9b show twoGaussian pyramid. Pyramid construction hasdient-based edge-detection technique can pictures of a circuit board taken with thethe effect of integrating the input valuesbe used to locate the boundary betweencamera focused at two different depth-within a set of Gaussian-like windows ofimage regions, Fig. 7d. (Pyramid levelsplanes. We wish to construct a compositemany scales (Stage 3).have been expanded to the size of the orig-image in which all the components and

the board surface are in focus. Let LA and As an example, integrated property esti-inal image to facilitate comparison.)

mates have been used to locate the boun-A third class of analysis operations con-LB be Laplacian pyramids for the two

dary between the two textured regions ofcerns fast coarse-fine search techniques.original images in our example. The low-Fig. 7a. The upper and lower halves of Suppose we need to locate precisely a largefrequency levels of these pyramids shouldthis image show two pieces of wood withcomplex pattern within an image. Ratherbe almost identical because the low spa-differently oriented grain. The right half ofthan attempt to convolve the full patterntial-frequency image components are onlythe image is covered by a shadow. Thewith the image, the search begins by con-slightly affected by changes in focus. Butboundary between the shaded and unshad- volving a reduced-resolution pattern with changes in focus will affect node values ined regions is the most prominent feature ina reduced-resolution copy of the image.the pyramid levels where high-spatial-the image, and its location can he detectedThis serves to roughly locate possible oc-frequency information is encoded. How-quite easily as the maximum of the gra-currences of the target pattern with a mini-ever, corresponding nodes in the two py-dient of the image intensity (Fig. 7b). How-mum of computation. Next, higher-resolu-ramids will generally represent the sameever, a simple edge-detecting operation suchtion copies of the pattern and image can feature of the scene and will differ primar-as this gradient-based procedure cannot bebe used to refine the position estimatesily in attenuation due to blur. The node used to locate the boundary between the through a second convolution. Computa-with the largest amplitude will be in thetwo pieces of wood. Instead it would iso- tion is kept to a minimum by restricting image that is most nearly in focus. Thus,late the line patterns that make up the the search to neighborhoods of the points\"in focus\" image components can be se-wood grain.identified at the coarser resolution. Thelected node-by-node in the pyramid ratherThe texture boundary can be foundsearch may proceed through several stagesthan region-by-region in the original im-through the three-step process as follows: of increased resolution and position refine-ages. A pyramid LC is constructed for theA Laplacian pyramid is constructed for ment. The savings in computation that composite image by setting each node equalthe original texture. The vertical grain ismay be obtained through coarse-fine searchto the corresponding node in LA or LB then enhanced by convolving the imagecan be very substantial, particularly whenthat has the larger absolute value:with a horizontal gradient operator (Stagesize and orientation of the target pattern

If |Lal (i,j) | > | LEl (i,i) |,

1). Each pyramid node value is then and its position are not known.

then LCl (i,j) = LAl (i,j)

squared, (Stage 2) and a new integration

otherwise. LCl (i,j) = LBl (i,j)

pyramid is constructed for each level of

(7)the filtered image pyramid (Stage 3). In Image enhancement

this way energy measures are obtainedThus far we have described how pyramidThe composite image is then obtained sim-within windows of various sizes. Figure 7cmethods may be applied to data compres-ply by expanding and adding the levels ofshows level 2 of the integration pyramid sion and image analysis. But there are otherLC. Figure 9c shows an extended depth-of-for level L0 of the filtered-image pyramid.areas of image science where thesefield image obtained in this way.

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RCA Engineer • 29-6 • Nov/Dec 1984

Fig. 7. Texture boundary detection using energy measures. The original image, (a),Fig. 8. Multiresolution coring. Part (a)contains two pieces of wood with differently oriented grain separated by a horizon- shows an image to which noise has tal boundary. The right half of this image is in a shadow, so an attempt to locate been added to simulate transmission

degradation. The Laplacian pyramid wasedges based on image intensity would isolate the boundary of the shadow region,

constructed for this noisy image, and(b). In order to detect the boundary between the pieces of wood in this image we

values at each level were \"cored.\"first convolve each level of its Laplacian pyramid with a pattern that enhances node

vertical features. At level L0 this matches the scale of the texture grain on the lowerAs a result, much of the noise is re-moved while prominent features of thehalf of the image. The nodes at this level are squared and integrated (by construct-

original image are retained in the re-ing an additional pyramid) to give the energy image in (c). Finally, an intensity

constructed image, (b).edge-detector applied to the energy image yields the desired texture boundary.A related application of pyramids con-cerns the construction of image mosaics.

This is a common task in certain scientificfields and in advertising. The objective isto join a number of images smoothly into alarger mosaic so that segment boundar- ies are not visible. As an example, supposewe wish to join the left half of Fig. 10awith the right half of Fig. 10b The mostdirect method for combining the images isto catinate the left portion of Fig. 10a withthe right portion of Fig. 10b. The result,shown in Fig. 10c, is a mosaic in which the boundary is clearly visible as a sharp(though generally low-contrast) step in graylevel.

This dilemma can be resolved if eachAn alternative approach is to join image

components smoothly by averaging pixelimage is first decomposed into a set ofvalues within a transition zone centered onspatial-frequency bands. Then a bandpassthe join line. The width of the transitionmosaic can be constructed in each band zone is then a critical parameter. If it is by use of a transition zone that is compar-too narrow, the transition will still be vis-able in width to the wavelengths repres-ible as a somewhat blurred step. If it is tooented in the band. The final mosaic is thenwide, features from both images will beobtained by summing the component band-visible within the transition zone as in apass mosaics.

The computational steps in this \"multire-photographic double exposure. The blur-solution splining\" procedure are quite sim-red-edge effect is due to a mismatch of

low frequencies along the mosaic boun-ple when pyramid methods are used.6 Todary, while the double-exposure effect is begin, Laplacian pyramids LA and LB aredue to a mismatch in high frequencies. Inconstructed for the two original images.general, there is no choice of transitionThese decompose the images into the re-zone width that can avoid both defects.quired spatial-frequency bands. Let P be the

39

Adelson et al.: Pyramid methods in Image processing

Fig. 9. Multifocus composite image. The original images with limited depth of field summed to yield the final mosaic, Fig. 10d.are shown in (a) and (b). These are combined digitally to give the image will anNote that it is not necessary to average nodeextended depth of field in (c).values within an extended transistion zone

since this blending occurs automatically aspart of the reconstruction process.

Conclusions

The pyramid offers a useful imagerepresentation for a number of tasks. It isefficient to compute: indeed pyramidfiltering is faster than the equivalentfiltering done with a fast Fourier transform.The information is also available in aformat that is convenient to use, since thenodes in each level represent informationthat is localized in both space and spatialfrequency.

We have discussed a number of examplesin which the pyramid has proven to bevaluable. Substantial data compression(similar to that obtainable with transformmethods) can be achieved by pyramidencoding combined with quantitization andentropy coding. Tasks such as textureanalysis can be done rapidly andsimultaneously at all scales. Severaldifferent images can be combined to form aseamless mosaic, or several images of thesame scene with different planes of focuscan be combined to form a single sharplyfocused image.

Because the pyramid is useful in so manytasks, we believe that it can bring someconceptual unification to the problems of

Fig. 10. Image mosaics. The left half of image (a) is catinated with the right half ofrepresenting and manipulating low-level

visual information. It offers a flexible,image (b) to give the mosaic in (c). Note that the boundary between regions is clearly visible. The mosaic in (d) was obtained by combining images separately in convenient multiresolution format thateach spatial frequency band of their pyramid representations then expanding andmatches the multiple scales found in the

visual scenes and mirrors the multiple scalessumming these bandpass mosaics.of processing in the human visual system.locus of image points that fall on theboundary line, and let R be the region to theleft of P that is to be taken from the leftimage. Then the pyramid LC for thecomposite image is defined as:If the sample is in R, then

40

LCl (i,j) = LAl (i,j)

If the sample is in P,then

LCl (i,j) = LBl (i,j),

Otherwise,

LCl = LCl (i,j) (8)

The levels of LC are then expanded and

References

1. H. Wilson and J. Bergen' \"A four mechanism modelfor threshold special vision\Vision Research. Vol.19, pp. l9-31, 1979.

RCA Engineer • 29-6 • Nov/Dec 1984

2. C. Anderson, \"An alternative to the Burt pyramid al-4. P. Burt, X. Xu and C. Yen, \"Multi-Resolution Flow-gorithm\

Through Motion Analysis, \" RCA Technical Report,3. P Burt and E. Adelson, \"The Laplacian Pyramid as aPRRL-84-TR-009, 1984.Compact Image Code,\" IEEE Transactions onCommunication, COM-31 pp. 532-540, 1983a.

5. J. Ogden and E. Adelson, \"Computer Simulations ofAuthors, left to right: Bergen, Anderson, Adelson, Burt.Edward H. Adelson received a B.A. degree,standing at New York University (1976-1978),summa cum laude, in Physics and PhilosophyBell Laboratories (1978-1979), and the Univer-from Yale University in 1974, and a Ph.D.sity of Maryland (1979-1980). He was a

degree in Experimental Psychology from themember of the engineering faculty at Rensse-University of Michigan in 1979. His dissertationlaer Polytechnic Institute from 1980 to 1983. Indealt with temporal properties of the photore-1983 he joined RCA David Sarnoff Researchceptors in the human eye. From 1978 to 1981Center as a Member of the Technical Staff,Dr. Adelson did research on human motionand in 1984 he became head of the Advancedperception and on digital image processing asImage Processing Group.a Postdoctoral Fellow at New York University.Contact him at:

Dr. Adelson joined RCA Laboratories in 1981RCA Laboratoriesas a Member of the Technical Staff. As part ofPrinceton, N.J.the Advanced Image Processing ResearchTacnet: 226- 2451

group in the Advanced Video Systems Re-search Laboratory, he has been involved inCharles H. Anderson received B.S. degree indeveloping models of the human visual sys-Physics at the California Institute of Tech-tem, as well as image-processing algorithmsnology in 1957, and a Ph. D. from Harvardfor image enhancement and data cUniversity in 1962. Dr. Anderson joined theompression.

staff of RCA Laboratories, Princetion, NJ, inDr. Adelson has published a dozen papers on1963. His work has involved studies of thevision and image processing, and has madeoptical and microwave properties of rare-numerous conference presentations. Hisearth ions in solids. These studies have pro-awards include the Optical Society of Ameri-duced an optically-pumped mirowave maserca's Adolph Lomb medal (1984), and an RCAand a new spectrometer for acoustic radia-Laboratories Outstanding Achievement Awardtion in the 10-to 300-GHz range.

(1983). He is a member of the Association forIn 1971 he was awarded an RCA fellowship

Research in Vision and Opthalmology, theto do research at Oxford University for a year, andOptical Society of America, and Phi Betain 1972 became a Fellow of the AmericanKappa.

Physical Society. Upon returning to RCA, heContact him at:

became involved in new television displays.RCA LaboratoriesBetween 1973 and 1978 he was a leader of aPrinceton, N.J.subgroup developing electron-beam guidesTacnet: 226-3036

for flat-panel television displays. In March1977 he was appointed a Fellow of the Tech-Peter J. Burt received the B.A. degree in Phys-nical Staff of RCA Laboratories.

ics from Harvard Unversity in 1968, and theFrom August 1978 through December 1982M.S. degree from the University of Massachu-he was head of the Applied Mathmaical andsetts, Amherst, in 1974 and 1976, respectively.Physical Sciences group. In January 1983 heFrom 1968 to 1972 he conducted research inreturned full time to research as a member ofsonar, particularly in acoustic imaging devices,the Vision Group, while maintaining a role asat the U.S. Navy Underwater Systems Center,a task force leader in studies of the stylus/New London, Conn. and in London, England.disc interface. In January 1984 he spent 5

As a Postdoctoral Fellow, he has studied bothweeks as a Regents Lecturer at the invitation ofnatural vision and computer image under-

the Physics Department of UCLA. This was

Adelson et al.: Pyramid methods in image processing

Oriented Multiple Spatial Frequency Band Coring,\"in preparation, 1984.

6. P. Burt and E. Adelson, \"Multiresolution Spline withApplication to Image Mosaics.\" ACM Transactionson Graphics, Vol. 2, pp. 217-236, 1983b.

Joan Ogden received a B.S. in Mathematicsfrom the University of Illinois, Champaign-Urbana in 1970, and a Ph.D. in Physics fromthe University of Maryland in 1977. Coming tothe Princeton Plasma Physics laboratory as aPost-Doctoral research associate, she con-tinued her work in nuclear fusion, special-izing in plasma theory and simulation. In1980, she started her own consulting com-pany, working on a variety of applied physicsproblems. In December 1982, she beganworking with the Advanced Image Process-ing Research Group, and has recently joinedRCA as a part-time Member of the TechnicalStaff. Her research interests at RCA includeapplications of the pyramid algorithm to pro-blems of noise reduction, data campression,and texture generation.Contact her at:

RCA LaboratoriesPrinceton, N.J.

did research into and developed a model ofthe structure of the primate visual systemfrom the retina to the striate cortex. Researchwas also done on the Hopfield model ofassociative memory.Contact him at:

RCA LaboratoriesPrinceton, N.J.Tacnet: 226-2901

James R. Bergen received the B.A. degree inMathematics and Psychology from the Univer-sity of California, Berkely, in 1975, and thePh.D. in Biophysics and Theoretical Biologyfrom the University of Chicago in 1981. Hiswork concerns the quantitative analysis ofinformation processing in the human visualsystem. At the University of Chicago he wasinvolved in the development of a model of thespatial and temporal processing that occurs inthe early stages of the system. From 1981 to1982 he was with Bell Laboratories, MurrayHill, N.J. His work concentrates on the effect ofvisual system structure on the extraction ofinformation from a visual image. His currentwork includes basic studies of visual percep-tion as well as perceptual considerations fordesign of imaging systems.Contact him at:

RCA LaboratoriesPrinceton, N.J.Tacnet: 226-3003

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