A Hierarchical Likelihood Classifier With Applications to Remote Sensing

Transcription

1 1th WSEAS International Conference on COMMUICATIOS, Heralion, Greece, July 3-5, 8 A Hierarchical Lielihood Classifier With Applications to Reote Sensing E. A. YFATIS Iage Processing Laboratory School of Coputer Science University of evada, Las Vegas, V, USA Abstract: In any classification, pattern recognition, segentation, probles, the subspaces the union of which fors the space of interest, have soe unique characteristics, and soe coon characteristics. The unique characteristics are expressed by one or ore features. otice that the nuber of features per unique characteristic is not fixed. The unique characteristics are used first to divide the space into subspaces in general larger than the target subspaces. Each subspace could contain one or ore of the final or target subspaces. If it is only one the recognition is finished, else we continue with the coon. Using the coon features we create a axiu lielihood classifier to axiize the probability of correct classification and iniize the probability of isclassification. We apply our theory here in a reote sensing environent. The ultichannel caera is ounted on an unanned aircraft, the signals are digitized using our analog to digital hardware, copressed lossless and transitted wireless, to a file server on earth, the caera is controled reotely. Key-Words: Statistical Pattern Recognition, Segentation, Classifiers, Reote Sensing, Deadalus Caeras. 1 Introduction In any classification, pattern recognition, segentation, probles, a group of one or ore subspaces the union of which fors the space of interest, have soe unique characteristics, and soe characteristics which are coon to all subspaces of the space. The unique characteristics are expressed by one or ore features. otice that the nuber of features per unique characteristic is not fixed. The unique characteristics are used first to divide the space into interediate subspaces in general larger than the target subspaces, but saller than the whole space. Each interediate subspace could contain one or ore of the final or target subspaces. If it is only one the recognition is finished, else we continue with the coon. Using the coon features we create a axiu lielihood classifier to axiize the probability of correct classification and iniize the probability of isclassification. We apply our theory here in a reote sensing environent. The ultichannel caera is ounted on an unanned aircraft, the signals are digitized using our analog to digital hardware, copressed lossless and transitted wireless, to a RAID-6 file server on earth. For exaple soe characteristics we have used in the past in the process of recognizing English language characters we consider as initial characteristics [6-7], the horizontal and vertical projections, if the character has zero, one or two loops, if the character has straight lines or curvy lines, or both straight and curvy, the nuber of connections the character has. Thus if the vertical projection of the character has a sall nuber of pixels in the top followed by epty pixels, followed by a relatively larger nuber of pixels bellow, and in addition to that has a sall horizontal projection then it is a sall i, or a sall j. On the other hand a character with two loops is a B. The first interediate subspace includes two target subspaces naely i, and j, where as the second ISS: ISB:

2 interediate subspace only includes one target subspace naely B. The architecture of the ultichannel caeras consists of a pris and lenses that analyze the white light into any frequencies provide polarization that enables capturing of any frequency channels of light. The presence of various pollutants, particles, etc in the atosphere affect the various frequencies of the light differently. Inversely by looing at the signals of the frequency bands obtained by the ultichannel caera we can infer what ind of particles the light encountered in its path. The classifier we constructed taes as input a nuber of features soe are spatial, soe are teporal, soe are frequency doain, soe are wavelet doain, and soe are discrete cosine doain features. The classifier is a lielihood estiate classifier which finds the lielihood function and coputes which one of the candidate spaces axiizes the lielihood function. Therefore based on the input features provides as output which space are ore liely these input features to belong to. There are several ultispectral iaging caeras [1], soe of those are the Aerial Caera Systes (ARC) which can carry a variety of fil caera systes, any of which are calibrated for precision photograetry. The Airborne Visible and Infrared Iaging Spectroeter (AVIRIS) with four bands having wavelength fro.41 μ to.45 μ. The Moderate Resolution Iaging Spectoeter (MODIS). The MODIS Airborne Siulator (MAS), which records fifty spectral bands with wavelength fro.4451 μ to μ. An iaging spectroeter siilar to the MAS is the MODIS Airborne Siulator ARC (MASTER) its theral bands are close to the ASA Advances Spaceborne Theral Eission and Reflection Radioeter satellite instruent which is designed to study the geologic and other Earth surface properties, it has fifty spectral bands fro.44 μ to.47 μ. The Airborne Multi-angle Iaging SpectroRadioeter (AirMISR) is an airborne instruent for obtaining ultiangle iagery to study the Earth s ecology and cliate. The Airborne Synthetic Aperture Radar, it acquires data siultaneously in the L, P, and C bands in ultiple polarizations. The instruent supports the Space Shuttle Iaging Radar-C (SIR-C), and is very widely used in the reote sensing counity. The Theatic Mapper Siulator is the Daedalus AADS- 168 scanner is ounted on aircraft and siulates the LADSAT TM instruent. It has several extra bands and slightly higher resolution than the LADSAT TM. The wavelength of its bands are fro.4 μ to14. μ, the quantization of the bands are 8-bits. The theral calibration of the instruent is achieved by blacbody sources carried on board. The Aiborne Ocean Color Iager (AOCI) is build by Daedalus Enterprises and is a high altitude ultiscanner used for oceanographic reote sensing. It has 1 bands, eight of which are quantized using 1 bits, with wavelength.436 μ to.897 μ. The last two are quantized using 8-bits. Their wavelength is fro.989 μ to 1.79 μ. The Multispectral Atospheric Mapping Sensor (MAMS) is a odified Daedalus scanner ounted on aircraft. In addition to the eight silicon detector channels in the visible and near infrared region found on the Daedalus Theatic Mapper Siulator, it has four channels in the infrared for studying weather related phenoena, such as cloud-top teperatures, upper atospheric water vapor, stor syste structure, etc. The wavelength of its 1 bands are fro.45 μ to 1.8 μ. The Electro-Optic-Caera is a three channel fraing caera. The channels include the green, red, and near IR part of the light spectru. The wavelength of the channels are fro.55 μ to.85 μ. The Satellite Teleetry and Return Lin (STARLin) syste transits realtie sensor data via the ASA Tracing and Data Relay Satellite Syste (TDRSS). It transits at 48 Mb/sec of data to the ground station and 4 Kb/sec bac to the aircraft for sensor control. The data is captured in RAIDarrays. Our contribution is in the video capture, video classification, lossless video copression, video transission, and reote caera control. The features are exctracted based on their ability to discriinate between environents with different coposition. In this experient the syste was used to discriinate between heavily polluted environents and environents far away fro industrial pollutants. The proble consists of several 1th WSEAS International Conference on COMMUICATIOS, Heralion, Greece, July 3-5, 8 ISS: ISB:

3 parts; including instruentation, video capture and analog to digital conversion, noise source identification, error correction and noise filtering, data analysis and data interpretation, lossless data copression and archiving. There have been any research papers published related to error correction angular sensitivity of ultispecral line scanners [-5], and a great deal of wor in reoving the between-swath radioetric variations by using the radioetric inforation contained in the overlapping region of swaths. More wor is needed in the iage processing, video processing, noise filtering, ultivariate spatial and teporal processing, teporal frae processing for changes over tie and change source identification The Hierarchical Classifier One of the ost popular data acquisition echaniss is the Daedalus MAMS The Multispectral Atospheric Mapping Sensor. All bands are quantized using 8-bits thus the aplitude is between and 55. Also onboard blacbody sources are carried for theral calibration. The atosphere consists of nitrogen oxygen, and various particles and pollutants. The nitrogen and oxygen absorb the higher wavelengths (low frequencies) and proote the lower wavelengths (higher frequencies). Thus the red colors suffer higher absorption than the green colors which suffer higher absorption than the blue colors. Thus in a clean atosphere the probability distribution of the red colors has relatively sall ean, while the probability distribution of the green colors has ean higher than the ean of the red, and the probability distribution of the blue has ean higher than that of the green. In a clean environent the probability distribution functions for the red, green and blue of the clean sy do not overlap. As the environent is increasingly polluted then depending on the type of pollutants, there is a shift of the probability distribution function of the frequency bands. Car pollution for exaple introduces any carbonic aterial which absorb the high frequency bands reduce the aplitude of the high frequency bands, thus shifting the ean of those bands towards the ean of the aplitude of the low frequency bands. This is the reason that as the sun sets in highly polluted areas the sy appears to have orange to red type of colors. The shift of the ean of the probability distribution of the 1 frequency bands depend on the type of pollutants and the aount of pollution in the atosphere. Scanning the clean sy above arid lands with low huidity the shape of the probability distributions of the bands are the sae, the variance therefore are not significantly different. As pollutants are introduced in the environent not only the ean of the probability distribution function is being shifted but the variances change. So the initial feature that reduces the space into a uch saller interediate subspace is the shift of the probability distribution in each one of the twelve bands. The ultichannel iages are divided into regions of interest. A region of interest is one for which there is a shift of the aplitudes for at least one band. For that region of interest the difference between pairs of bands are obtained and the probability distribution functions of the differences is estiated. Certain substances in the ground and therefore in the atosphere produce probability distribution functions of the differences which are very characteristic to the presence of that substance. If we assue that to corresponding pixels of two bands are independent and D is a rando variable denoting the difference of the two corresponding pixels then: 1th WSEAS International Conference on COMMUICATIOS, Heralion, Greece, July 3-5, 8 P(D = ) = 56/65,536, P(D = 1) = p(d = -1) = (56-1)/65,536, P( D = )= P( D = -) = ( 56-)/65,536, =,1,,, 55 () The expected value of the above discrete probability function is zero. In the presence of various substances, water vapors, plutoniu, uraniu, carbonic aterial and other pollutants, depending of which aterial are present, certain band differences depart fro the above ISS: ISB:

4 distribution in a way that is very characteristic to the presence of these substances and their intensity. This space series analysis is cobined with frequency doain ethods. If the probability distribution function is the one given in () then the Fourier transfor would be: 55 n= 55 π n 511 A = P( D= n) e, =-55,,,,55, (3) 1th WSEAS International Conference on COMMUICATIOS, Heralion, Greece, July 3-5, 8 The spectral density is S = AA, =- 55,, -1,,1,,55 (4) The phase spectru is: I( A ) ϕ = arctan( ), =-55,,,, Re( A ) 55, (5) The presence of substances changes the spectral density of the differences of certain bands. The change is very characteristic to the substances present. Any changes in the ground has an ipact in the atosphere and causes discontinuities in ost spectral bands, thus gradient ethods with phase inforation are extreely useful in correctly identifying freshly disturbed ground, or new concrete being poured, eission of radioactive aterial, etc. Wavelet analysis provides useful tools for pattern recognition. Wavelets were introduced in the early 198's as a tool for signal analysis by the French geophysicists T. Morlet at Elf- Aquitoe for the analysis of seisic data. There is a strong relationship between wavelets and the singular integral operators. In 1988 Ingrid Daubechis constructs failies of orthonoral wavelets with copact support. Wavelets consist of a set of functions generated by a siple function, using two paraeters a, b one for position and the other for scaling or dilation. Thus starting with g (x) we derive: = 1/ x a g a, b ( x) b g, b, a, b R b (6) We constraint g ( x) L ( R) which iplies G( ω) dω < + (7) ω + i x Where G( ω) = g( x) e ω dx (8) g(x) The ean value of the wavelet is zero. Or + g ( x) dx = (9) f = ϕ 1, p (1) p Let f (t), < t < +, then the Fourier transfor F( ϖ ) of f (t) could be defined as + jωt F( ϖ ) = f e dt (11) The above represents an average analysis, since integration is an averaging operation over tie t. The Fourier analysis gives us all the frequency coponents and provides excellent localization in frequency, but fails to associate frequency coponents with the tie of occurrence. The function f (t) gives a tie representation of the inforation while F (w) represents the sae inforation in the frequency doain. A function f (t), < t < + can be expressed us as f = w, ψ, (1) If ψ, are orthogonal, naely if + ψ, ψ, dt = 1, if = (13) and = zero otherwise. 1 ψ = ψ ( ( t )) (14), The Discrete Wavelet Transfor is used for ultilevel decoposition of an input iage into high and low frequency coponents in different resolutions. The DWT decopositions provide edge detection of iages in the horizontal, vertical and diagonal directions; decopositions preserve sooth texture and enhance coarse texture. DWT texture analysis of 1 bands ranging fro visible color to near IR, is copared with distribution of 1-band histogras. ISS: ISB:

5 The two-diensional discrete wavelet transfor (D DWT) is an extension of the one-diensional transfor. They are siply ipleented by using onediensional DWT s along each diension n and separately: DWT nx [x[n,]] = DWT n [DWT [x[n,]] In this way, separable two-diensional filters are only considered. There are several versions of the DCT. Types II and III have received a great deal of attention in digital iage processing. The DCT transforations are real, orthogonal, separable and have properties relevant to data classification and fast algoriths for its coputation. Another transfor used in transfor theory is the DST. In the DCTs and DSTs described below is an integer power of. subband D()=, SPIHT eeps trac of the states of sets of indices by eans of three lists. The list of insignificant sets (LIS) The list of insignificant pixels (LIP) The list of significant pixels (LSP) For each list a set is identified by a single index. In the LIP and LSP these indices represent the singleton sets {} where is the identifying index. 1th WSEAS International Conference on COMMUICATIOS, Heralion, Greece, July 3-5, 8 An index is called significant if the transfor value w() is significant, or insignificant if w() is insignificant. For the LIS, the index denotes either D() or G(). If denotes the D() is called type D, and if denotes G is called type G. In the following we denote the ST as S. significance function The discrete Fourier transfor (DFT) and the inverse DFT for a pair of orthogonal transfors. DCT I : (15) F = n n= x C C n π n cos, =,1,..., 1 The Modified Set Partitioning in Hierarchical Trees algorith can be used for iage classification and can be described using the following notation. For a given coefficient at location [ i, j ] let C [ i, j ] be the set of its children, let D [ i, j ] be the set of its descendents, and let G [ i, j ] be the set of its grandchildren and great grandchildren, etc. (i.e., G[ i, j ] = D[ i, j ] C[ i, j ] ). The Algorith can be used to correctly classify iages. For a given set I of indices in the baseline scan order the significance S T [I] of I relative to a threshold T. 1if ax[ w( n)] T ST ( I) = { (16) if ax[ w ( n )] < T ST [ I ] = indices D() = {Descendent indices of the index } C() = {Child indices of the index } G() = D() C() = {Grandchildren of } The set H consists of indices for the L th level where L is the nuber of levels in the wavelet. The indices in the all low-pass subband have no descendants. So if is in the all low-pass. x n = = n= 1 = x e n e π n j π n j (17) The eleents of the sequence, 1,, K, 1 are called the Fourier, spectral lines, and =,1,, K, 1, is called the spectru or spectral density. The arbitrary spectral line, =,1,, K, 1, can be represented as jϕ ( ) = e, =,1,, K, 1. (18) The angle ϕ ( ), =,1,, K, 1, is called the phase spectru, ( ) n ϕ. -D Fourier transfors over the iage space, and 3-D Fourier transfors over space and tie for each band could provide phase differences, and frequency changes that are due to ground cover changes. Furtherore crosscorrelation between frequency bands and ultivariate ethods to include all bands as a ultidiensional vector over tie could increase the recognition ability significantly. ISS: ISB:

6 Looing at the probability distribution of the bands pertaining to desert we conclude that the characteristic bands of Desert are bands 3, 5, 8, 9 and 1 are closely correlated over a sall range. Bands 1, and 4 are very closely correlated over a sall range. The predoinant visible bands are 5 and 1. Since desert sand has high theral energy, bands 11 and 1 are always the ost predoinant, widely distributed bands. 3. Conclusion Choosing the proper initial feature vector we divide the initial large space into a uch saller subspace. If this subspace includes ore than one target space the lielihood classifier using the features coon to all subspaces is applied using. The unique characteristics are expressed by one or ore features. otice that the nuber of features per unique characteristic is not fixed.. Each interediate subspace could contain one or ore of the final or target subspaces. If it is only one the recognition is finished. Using the coon features we create a axiu lielihood classifier to axiize the probability of correct classification and iniize the probability of isclassification. We apply our theory here in a reote sensing environent The input of ultichannel caeras is being affected differently by different substances in the ground and the atosphere. The initial vector consists of the 1 arginal probability distribution functions of the frequency bands. The coon features are the teporal, frequency doain, wavelet doain and discrete cosine transfor features. The lielihood function is estiated. The space which axiizes the lielihood function is the one that the input vector belongs to. References [1] Sensor Systes of the ASA Airborne Science Progra ASA Dryden Flight Reaserch Center.. []. G. J. Davison, Ground Control Pointing and Geoetric Transforation of Satellite Iagery, International Journal of Reote Sensing, Vol. 7, o. 1, pp , 1986 [3]. M. Ehlers, Rectification and Registration., In Integration of Geographic Inforation Systes and Reote Sensing, Cabridge University Press, Cabridge, UK, chapter, pp , 1997 [4] R. Richter. A. Muller, and U. Helden, Aspects of operational atospheric correction of hyperspectal iagery, International Journal of Reote Sensing, vol. 3, pp ,. [5] E. A. Yfantis, The Future of Digital Iage Processing and Digital Video, Key ote Speech, IEEE- Coputer Society, ICIIS-99, Bethesda Maryland, ov. 1-3, [6] J. Tse, D. Curtis, C. Jones, and E. Yfantis, An OCR Independent Character Segentation Using Shortest Path in Grayscale Docuent Iages, Sixth IEEE Intern. Conf. on Machine Learning and Applications, Cincinnati Ohio, Dec , 7, pp [7] D. Curtis, V. Kubushyn, E. A. Yfantis, and M. Rogers, A Hierarchical Feature Decoposition Clustering Algorith for Unsupervised Classification of Docuent Iage Types, Sixth IEEE Intern. Conf. on Machine Learning and Applications, Cincinnati Ohio, Dec , 7, pp th WSEAS International Conference on COMMUICATIOS, Heralion, Greece, July 3-5, 8 ISS: ISB: