statistical filter for image feature extraction

Statistical filter for image feature extraction

H. C. Schau

Edge extraction techniques have become important as a preprocessing step in extraction of image featuresfor the purpose of image segmentation, object identification, and bandwidth compression. The use of con-ventional edge extractors such as Sobel and Laplacian filters results in images that in many cases have a highdegree of clutter due to the natural spatial texture of the scene background. To overcome this difficulty,a statistical filter has been developed that enhances local grey level activity around objects while reducingcontributions due to background. The statistical filter is employed in a neighborhood modification processwhere the central pixel is replaced with the third central moment computed from the surrounding neighbor-hood. Choice of the third central moment is due in part to the fact that it is a function of the scene withinthe neighborhood rather than the power spectral density (Wiener spectrum) of the neighborhood. Applica-tion of the filter requires no prior knowledge, and pixels within the filter window may be chosen in randomorder due to the statistical nature of the operation. Results of the filter applied to IR images show perfor-mance comparable with, and in some cases superior to, the Sobel and Laplacian filters most commonly usedfor feature and edge extraction.

1. Introduction

There are many applications in image processing inwhich it is desirable to process an image so that partic-ular objects stand out in the resulting scene. Examplesof such objects might be buildings, people, vehicles,certain crops, and tumors. Generally the problemcomes about either in an attempt to assist an operatorviewing a monitor, where the problem is compoundedby a typically low dynamic range display and short timeinterval for viewing the scene, or in an autonomous in-spection system that must reduce the number of can-didate sites in the scene for further consideration dueto hardware constraints. In either case, simple pre-processing in the form of a filter can often substantiallyenhance features of interest and reduce clutter.

In applications where there are large amounts ofsensor noise, sequential adding of images can be effec-tive in reducing noise. When clutter is caused by thebackground, spatial smoothing is often attempted

The author is with General Research Corporation, 2018-C LewisTurner Boulevard, Fort Walton Beach, Florida 32548.

Received 29 November 1979.0003-6935/80/132182-09$00.50/0.© 1980 Optical Society of America.

analogous, for example, to a Hamming spectral windowin time series analysis.1 It is often the case that, be-cause clutter has some small but finite spatial correla-tion length, the dimensions of the filter are large enoughto cause appreciable resolution degradation. Thisworks a particular hardship in IR images in which theobjects appear somewhat blurred initially.

The common filters employed to enhance featuresmay be roughly divided into two classes, constrainedand unconstrained. 2 3 A constrained filter is designedto filter a class of objects from a class of clutter on thebasis of a given fidelity criterion. Typically the Wienerspectrum of target and background is required, and thefidelity constraint is the minimum square error. Ex-amples of such filters include Wiener filters, leastsquares filters, and maximum entropy filters. Thedisadvantages of these filters are that although theirachievements are often impressive, they require a prioriknowledge, often not available, and are somewhat dif-ficult to implement.

The other class of filters which are more commonlyseen are unconstrained filters. These filters have aspecific filtering function and perform their task on allinputs without regard to any outside stimulus. Un-constrained filters may be linear such as the Laplacianand Hamming or nonlinear such as the median orSobel. 3

This paper describes a new unconstrained filter andcompares results with some common unconstrained

2182 APPLIED OPTICS / Vol. 19, No. 13 / 1 July 1980

Fig. 1. Sequence of six IR (8-14 -gm) images. Each image is 512 X 512 pixels where data is contained in 8 bits.

1 July 1980 / Vol. 19, No. 13 / APPLIED OPTICS 2183

Fig. 2. Resultant of applying a Sobel operator to Fig. 1.


Fig. 3. Resultant of applying a Laplacian operator to Fig. 1.

- 1 July 1980 / Vol. 19, No. 13 / APPLIED OPTICS 2185

Fig. 4. Resultant of applying the third central moment operator to Fig. 1.


- I I I- --- --�, , ��, �,� - -

1�

It'; 1� I I

filters. The performance of the new filter is appreciablybetter for many applications than common edge de-tectors or Laplacian operators, and implementation iskept simple.

II. Third Central Moment Filter

The new unconstrained filter we wish to discuss is onethat computes the third central moment of a neigh-borhood and replaces the central pixel with that value.This technique of a statistical neighborhood modifica-tion process may be written as

XI =-E (Xj X)3 , (1)Awindow

where Xi is the output value, Xj is an arbitrary valuewithin the window, X is the mean of the randomvariable X within the window, and A is the area of thewindow. As shown in Eq. (1), the location of the valuesof Xj within the window is arbitrary and may be chosenin any order. This eases implementations, since the

order of pixels within the window may be chosen to bethe most convenient for each application. Filter outputmay be either positive or negative, and implementationrequires no prior information (except window size whendesired).

The rationale behind the choice of employing thethird central moment is given elsewhere.4 For thepurposes of this paper it suffices to state that the thirdmoment is the lowest moment in the intensity distri-bution density function that is unique to the actualscene within the window. Lower-order moments areunique only to the Wiener spectrum, which often isquite similar for both object and background. Thethird moment depends on the complex spatial fre-quency spectrum of the window, which can be quitedifferent for two windows having similar Wiener spec-tra. The rationale for the central moment is twofold;it allows both positive and negative values of the output,and it keeps output normalized to convenient num-erical values. 5

Fig. 5. Histograms of the 8-bit data for typical images. Left to right from upper left, the histograms represent the initial IR image, Sobeloperator, Laplacian operator, and third central moment operator.


Fig. 6. Modulus of the third central moment operator of Fig. 4. Only positive quantities are present in the representation.


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~0

CD

CZ~ ~ ~ ~~~~~~~~~~~~~~~~~~~dCIu -co C

C

CZ

o -~~~~~~~~~~~~~

00~~~~~~~~~~~~~~~~~~~~~~~~~~C

00~~~~~~~~~~~~~~~~

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CD

cc~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~c0~~~~~~~~~~~~~~~~~~~; Cd ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~b0cd C


IM

M�� R." � §O - IIM, I ��M N � � MpdANN P �

Ill. Results

Figure 1 shows a series of six 512 X 512 sequential IRimages (8-14 ,4m) taken at night after a rain (note theman on the road in the first image). Shown in Figs. 2and 3 are the results of spatial filtering with Sobel andLaplacian operators, respectively. The results indicatethe high degree of background clutter still remaining inthe images. Figure 4 shows the results of a 3 X 3neighborhood modification process where the thirdcentral moment of the neighborhood has replaced thecentral pixel. The clutter reduction is apparent, whiletank, buildings, and the man on the road show up quitewell. In displaying the grey level scenes and Sobel op-erator, the display was set to encompass the tails of the8-bit histogram of the data. This was difficult to at-tempt with the third central moment as shown by atypical third central moment histogram compared withthe other histograms in Fig. 5. In displaying the lasttwo operators we have set the center of the displaybrightness at the peak of the histogram and the highestand lowest values at three standard deviations on eitherside. This is a good compromise for the display, al-though it is clear that more optimal display look-uptables could be found.

It will be recalled that the output of the Sobel oper-ator is a positive definite quantity since it results fromthe square root of the sum of two filters squared. Tocompare the third central moment with the Sobel, wedisplayed the modulus of the output in Fig. 6. In thesefigures zero was set at the peak of the histogram (as withthe Sobel, Fig. 2), and maximum brightness was set atpositive and negative three standard deviations. Theresulting output is again very effective in extractingobjects of interest.

Another advantage of statistical filters is the abilityto implement any prior knowledge concerning objectsize or shape. This is done by simply changing thewindow size or shape to that desired. An analogousoperation may be performed in linear filtering bychanging window size to synthesize the bandpass of adesired transfer function. A simple example of thismay be seen in Fig. 7. This is a 128 X 128-pixel IRimage (8-14 tim) taken on a sunny day. The scene isrich in objects and texture (clutter). Of noteworthyinterest are the road (right side), tank (side view; right

center of image), tree line, tree trunk (lower left), tree'sshadow (lower left center), and an unknown hot objectseen through the trees (upper center). Figures 8 and9 show the results of Sobel and Laplacian operators onthis scene. Due to the large degree of clutter, particu-larly from leaves, there is expected to be substantialedge and Laplacian output as observed. Figure 10shows the results of a 7 X 7 third central moment filter.Note how the smoothing effects of the 7 X 7 filter en-hance activity of that size compared with the 3 X 3 filterof Fig. 11. Consider, for example, the detail within thetank body and at the vertex of the road. In the 7 X 7case this detail is lost to the enhancement of the overalllarge shape, but the 3 X 3 filter shows clearly thestructure of both cases.

IV. Conclusion

We have demonstrated that the use of the thirdcentral moment in a neighborhood modification processcan, in many instances, reduce clutter while enhancingobjects or their gradients. The use of the statisticalaspects of the local regions requires no prior informationfor useful implementation. It was demonstrated thatprior knowledge concerning shape or size may be em-ployed by choosing the neighborhood size similarly tochoosing the bandpass of a conventional linear filter.

It has been observed that the third central momentincreases intraclass separabilities better than conven-tional filters such as the Sobel or Laplacian for caseswhere the signal difference to noise (clutter) ratio isgreater than 1. This can be seen in Fig. 12 in which anintraclass distance measure similar to Mahalanobis'sdistance may be defined as

M = (target mean - background mean)2

variance of background

for a series of images similar to those in the precedingfigures. The results clearly indicate the superiority ofthe third central moment for cases in which M > 1. Thethird central moment yields inferior results for instanceswhere M < 1; however, in this regime, all techniquesdegrade class separabilities. Situations where M - 1require further analysis since the closest computed datapoint in Fig. 12 is M = 1.06.

The author would like to thank Keith Noren for as-sistance in computer programming and Charles Laynefor supplying the data of Fig. 12.

References1. R. B. Blackman and J. W. Tukey, The Measurement of Power

Spectra (Dover, New York, 1958).2. H. C. Andrews and B. R. Hunt, Digital Image Restoration

(Prentice-Hall, Englewood Cliffs, N.J., 1977).3. W. K. Pratt, Digital Image Processing (Wiley-Interscience, New

York, 1978).4. H. C. Schau, Appl. Opt. 19, 228 (1980).5. B. J. Schachter, L. S. Davis, and A. Rosenfield, Pattern Recognition

2,19 (1979).


statistical filter for image feature extraction

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