[DOCUMENT NAME] SPECIFICATION [TITLE OF THE INVENTION] IMAGE PROCESSING APPARATUS, METHOD, AND PROGRAM [TECHNICAL FIELD] [00011 The present invention relate sto animage processing apparatus and method for discriminating structure of a structure in an image, and a program for causing a computer to perform the image processing method. [ BACKGROUND ART 1 [0002] Recently, high quality three-dimensional images have been used in image diagnosis with the advancement of medical equipment ( e . g . , multidetector CT and the like) . As a three-dimensional image is formed of a multiple of two-dimensional images and has a large amount of information, the doctor may sometimes require a prolonged time to find out a desired observation region and give a diagnosis. Consequently, it is practiced to extract an organ of interest and perform MIP, VR, or CPR display, or the like, in order to enhance t.he visibility of an entire organ or a lesion and improve efficiency of diagnosis. [0003] In the meantime, as a method of extracting a blood vessel or a bone in a medical image, Hessian analysis using a Hessian matrix is proposed (refer to Non-Patent Document 1) . The Hessian analysis discriminates whether a local structure in an image is a point, a line, or a plane by analyzing eigenvalues of a Hessian matrix whose elements are second order partial differential coefficients calculated by the use of the second differential kernel of a given filter, such as Gaussian kernel or the like. The use of the Hessian analysis allows a blood vessel and a bone to be discriminated as a line-like structure and a plate-like structure respectively. [ 0004 I There are cases, however, in which, if another structure is presentinthevicinityofaline-like structure (vicinitystructure), the method of Non-Patent Document 1 erroneously discriminates the vicinity structure as the line-like structure. The method of Non-Patent Document 2 improves the filter proposed in Non-Patent Document 1 by convoluting a function representing a solid sphere (solid spheremodel function) with the inside ofthe spherical shape as 1 and the outside as 0 and limiting the calculation range of the second order partial differential coefficients to the surface of the sphereinHessiananalysis, wherebythe influenceofthevicinity structure on the filtering result may be reduced. [Prior Art Documents] [Non-Patent Documents] [0005] [Non-Patent Document 11 A. F. Frangi et. al., "Multiscale vessel enhancement filteringN, Proceedings of MICCAI, pp130-137, 1998 [Non-Patent Document 21 M. Law et. al., "Three Dimensional Curvilinear Structure Detection Using Optimally Oriented Flux", Proceedings of ECCV, pp368-382, 2008 \DISCLOSURE OF THE INVENTION] [PROBLEMS TO BE SOLVED BY THE INIENTION] [0006] If a blood vessel, which is a line-like structure, is discriminated from a medical image that includes blood vessels of various thicknesses using the method of Non-Patent Document 2, however, there may be a case in which a blood vessel narrower that an actual blood vessel is erroneously recognized inside a blood vessel. In other words, if a line-like structure is discriminated by the method of Non-Patent Document 2, there may be a problem that an erroneous discrimination is made at a portion of the contour of a structure having a radius of curvature greater than radius of curvature of a solid sphere of a solid sphere model function that a line-like structure having a diameter substantially the same as the diameter of the solid sphere represented by the solid sphere model function is present. [0007] The aforementionedproblenmaypossibly occur at any contour portion of a structure having a radius of curvature greater than the radius of curvatureofthe solidsphere ofthe solid spheremodel function. In view of the problem described above, therefore, it is an object of the present invention to prevent, in image processing method that performs filtering using a solid sphere model function in Hessian analysis, erroneous discrimination of structure that occurs at a contour portion of a structure having a radius of curvature greaterthanthe radius of curvature ofthe solid sphere represented by the solid sphere model function. [MEENS FOR SOLVING THE PROBLEMS] [0008] An imageprocessingapparatus according tothe first invention includes a filtering unit that performs filtering on each pixel position in an image using a second order partial differential of a function representing a solid sphere and calculates a Hessian matrix, and an evaluation unit that discriminates a structure included in the image using eigenvalues and eigenvectors obtained by performing eigenvalue analysis on the calculated Hessian matrix, wherein the filtering unit includes a correction unit that performs filtering on each pixel position in the image using a first order partial differential of a function representing a hollow sphere having the same radius as the radius of the solid sphere and obtains firstorderpartialdifferentialvectors, andcarries out correction to cancel out one of response waveforms of the second order partial differential of the function representing the solid sphere in each direction, the response waveforms appearing at two positions symmetrically separated with respect to the center of the solid sphere, using values obtainedbyprojectingthe obtained first order partial differential vectors onto directions of the eigenvectors. [0009] An image processing method according to the first invention includes a filtering step that performs filtering on each pixel position in an image using a second order partial differential of a function representing a solid sphere and calculates a Hessian matrix, and an evaluation step that discriminates a structure included in the image using eigenvalues and eigenvectors obtained by performing eigenvalue analysis on the calculatedHessianmatrix, wherein the filtering step performs filteringon eachpixelposition in the image using a first order partial differential of a function representing a hollow sphere having the same radius as the radius of the solid sphere and obtains first order partial differential vectors, and carries out correction to cancel out one of response waveforms of the second order partial differential of the function representing the solid sphere in each direction, the response waveforms appearing at two positions symmetrically separated with respect to the center of the solid sphere, using values obtained by projecting the obtained first order partial differential vectors onto directions of the eigenvectors . [OOlO] Note that the image processing method according to the first invention may be provided as a program for causing a computer to perform the image processing method. I OOll] The "hollow sphere having the same radius as the radius of the solid sphere" as used herein includes not only the case where the radii of the solid sphere and the hollow sphere strictly corresponds to each other but also the case where the radius of the hollow structure is greater or smaller than the radius of the solid sphere if it is within the range having an effect of cancelling out the response waveform at one position of response waveforms of the second order partial differential of the function representing the solid sphere in each direction, the response waveforms appearing at two positions symmetrically separated with respect to the center of the solid sphere, using the first order partial differential vectors. In order to satisfactorilyobtain the "effect of cancelling out the response waveform at one position", it is preferable that the radii of the hollow sphere and the solid sphere be equal as much as possible and, for example, the difference in radius between the hollow sphere and the solid sphere is preferably 20% or less and the difference in radius between the hollow sphere and the solid sphere is preferably 10% or less. 100121 In the image processing apparatus according to the first invention, if eigenvalues of the evaluation matrix are taken as All A2, A3, elgenvectors are taken as el= (XI, yl, zl), e2= ( ~ 2 , y2, 22) , e,= ( ~ 3 ,y3 , z3) , and the first order partial differential vectors of the function representing the hollow sphere are taken as (pl, pz, p j ) , the correction unit carries out the correction to cancel out the one of the response waveforms by correcting the eigenvalues as shown in Formula (13) given below using pl', p2' , p3! calculated by Formula ( 12) given below and a predetermined coefficient : 0 A,'= lf 1x1 1 < nlin(/ h, + apl I, I A, - ap; I ) otherwise [00131 In the image processing apparatus according to the first invention, the functionrepresentingthehollow sphere ispreferably represented by Formula (10) given below: where, x, y, z a r e t h e coordinates of three-dimensional space, r is the polar coordinate representation thereof, and R4 is the radius of the hollow sphere. [0014] An image processing apparatus according t o the second invention includes a f i l t e r i n g u n i t t h a t performs f i l t e r i n g on each pixel position in an image usinga secondorder p a r t i a l d i f f e r e n t i a l of a function representing a solid sphere and calculates a Hessian matrix, and an evaluation unit that discriminates a structure included in the image using eigenvalues and eigenvectors obtained by performing eigenvalue analysis on the calculatedHessianmatrix, wherein the f i l t e r i n g unit includes a correction u n i t t h a t p e r f o m f i l t e r i n g on each pixel position in the image using a f i r s t order p a r t i a l d i f f e r e n t i a l o f a functionrepresentingasecondsolidsphere havinga secondradius g r e a t e r t h a n a f i r s t r a d i u s w h i c h i s t h e radius of the f i r s t solid sphere and calculates f i r s t order p a r t i a l d i f f e r e n t i a l vectors, further performs f i l t e r i n g on each pixel position in the image using a f i r s t order p a r t i a l d i f f e r e n t i a l of a function representing a third s o l i d sphere having a third radius which is smaller than the f i r s t radius and calculates f i r s t order p a r t i a l d i f f e r e n t i a l vectors, and c a r r i e s out correction to cancel out a response waveform a t one position of response waveforms of the second order p a r t i a l d i f f e r e n t i a l of the function representing the solidsphereineachdirection, the responsewaveforms appearing a t two positions symmetrically separatedwith respect to the center of the solid sphere, using values obtained by projecting the f i r s t order p a r t i a l d i f f e r e n t i a l vectors of the function representing the second solld sphere onto directions of the eigenvectors and values obtained by projecting the f i r s t order p a r t i a l d i f f e r e n t i a l vectors of the function representing the third solid sphere onto directions of the eigenvectors. [0015] Preferably, in the image processing apparatus according to the second invention, the response waveform at the one position is a waveform in which one positive peak and one negative peak are -J2-2-2--. L . A. DECLARATION I, Eizo Yamagishi, of Yanagida & Associates, 7F Shin-Yokohama KS Bldg . , 3-1 8-3 Shin-Yokohama, Kohoku-ku, Yokohama-shi, Kanagawa, JAPAN, herebycertifythat theattached is my English translation of the certified priority document for JP 2012-056855, and certify that my translation is a true andcorrect translation to the best of my knowledge andbelief. C Dated this 10th day of September , 2014 and, for example, the difference between the second radius and the first length is preferably 20% o r l e s s and more preferably 10% or less. [001'7] Likewise, the "the thirdradius correspondstothelength from the center of the f i r s t solid sphere to the positive peak or the length from the center of the f i r s t solid sphere to the negative peak, whicheverislonger" includesnotonlythecasewherethethird radius corresponds s t r i c t l y t o the length from the center of the solid sphere to the positive peak or the length from the center of the solid sphere to the negative peak, whichever is shorter (second length), butalsothecasewherethethirdradiusisgreaterorsmaller than the second length i f it is within the range having an effect of cancelling out the response waveform at one position of response waveforms of the second order partial differential of the function representing the first solid sphere in each direction, the response waveforms appearing a t two positions symmetrically separated with respect tothe center ofthe solid sphere, usingthevectorsobtained by weighting the f i r s t order partial differential vectors of the functionrepresentingthethirdsolidsphereandthevectorsobtained by weighting the first order partial differential vectors of the function representing the t h i r d s o l i d sphere. In order to satisfactorily obtain the "effect of cancelling out the response waveform a t one position", it i s preferable that the third radius and the second length be equal as much as possible and, for example, the difference between the third radius and the second length i s preferably 20% or less and more preferably 10% or less. [0018] In the image processing apparatus according to the f i r s t invention, the filtering unit preferably calculates, with respect to functions representing the solid sphere in a plurality of sizes, an evaluation matrix by performing f i l t e r i n g with a second order partial differential matrix of a function representing each solid sphere. [00191 In the image processing apparatus according to the second invention, the filtering unit calculates, with respect to functions representing the first solid sphere in a plurality of sizes, an evaluationmatrixbyperfomingfilteringwithasecondorderpartial differential matrix of a function representing each of the first solid spheres. [00201 Preferably, in the image processing apparatuses according to the first and the second inventions, the image is a medical image and the structure is a blood vessel. 100211 Preferably, in the image processing apparatuses according to the first and the second inventions, the filtering unit performs the filtering using the second order partial differential matrix of the function representing the solid sphere in Fourier space. [0022] Preferably, in the image processing apparatuses according to the first andthe secondinventions, theevaluationunit discriminate at least one of local point-like, line-like, and plane-like structures of the structural object. [ADVANTAGEOUS EFFECTS OF THE INVENTION] [ 00231 According to the first invention, a filtering unit that performs filtering on each pixel position in an image using a second orderpartial differential of a function representinga solidsphere and calculates a Hessian matrix, and an evaluation unit that discriminates a structure included in the image using eigenvalues and eigenvectors obtained by performing eigenvalue analysis on the calculated Hessian matrix are provided, and the filtering unit includes a correction unit that performs filtering on each pixel position in the image using a first order partial differential of a function representing a hollow sphere having the same radius as the radius of the solid sphere and obtains first order partial differential vectors, and carries out correction to cancel out one \ 5 QCT of response waveforms of the second order partial differential of the function representing the solid sphere in each direction, the response waveforms appearing at two positions symmetrically separatedwithrespecttothecenterofthesolidsphere, usingvalues obtainedbyprojectingtheobtained first orderpartial differential vectors onto directions of the eigenvectors. This may inhibit erroneous discrimination that occurs when a contour portion of a structure having a radius of curvature greater than the radius of curvature of a solid sphere of a function representing the solid sphere corresponds to only one position of response waveform of the second partial differential of the function representing the solid sphere in each direction and the accuracy of the evaluation values may be improved. Consequently, a structure included in an image may be discriminated more accurately based on the evaluation values. [0024] According to the second invention, a filtering unit that performs filtering on each pixel position in an image using a second order partial differential of a function representing a solid sphere and calculates a Hessian matrix, and an evaluation unit that discriminates a structure included in the image using eigenvalues and eigenvectors obtained by performing eigenvalue analysis on the calculated Hessian matrix are provided, and the filtering unit includes a correction unit that performs filtering on each pixel position in the image using a first order partial differential of a function representing a secondsolidspherehaving a secondradius which is greater than a first radius, the first radius being the radius of the first solid sphere, and calculates first order partial differential vectors, further performs filtering on each pixel position in the image using a first order partial differential of a function representing a third solid sphere having a third radius which is smaller than the first radius and calculates first order partial differential vectors, and carries out correction to cancel out a response waveform at one position of response waveforms of the second order partial differential of the function representing the solid sphere in each direction, the response waveforms appearing at two positions symmetrically separated with respect to the center of the solid sphere, using values obtained by projecting the first order partial differential vectors of the function representing the second solid sphere onto directions of the eigenvectors and values obtainedbyprojectingthe first order partial differential vectors of the function representing the third solid sphere onto directions of the eigenvectors. This may inhibit erroneous discrimination that occurs when a contour portion of a structure having a radius of curvature greater than the radius of curvature of a solid sphere of a function representing the solid sphere corresponds to only one posltion of response waveform of the second partial differential of the function representing the solid sphere in each direction and the accuracyofthe evaluationvaluesmaybe improved. Consequently, a structureincludedinanimagemaybediscriminatedmoreaccurately based on the evaluation values. [BRIEF DESCRIPTION OF THE DRAWINGS] [0025] [Figure 11 A schematic block diagram of an image processing apparatus according to a first embodiment of the present invention, illustrating a configuration thereof l Figure 21 drawing forexplainingamultiple resolutiontransformation [Figure 31 Adrawing forexplainingeigenvalues of aline-like structure [Figure 41 Adrawingforexplainingeigenvaluesofaplane-like structure [Figure 5A] A drawing for explaining the principle of correction processingaccordingtothe first embodimentofthepresent invention [Figure 5B1 A drawing for explaining response of second order partial differential of a solid sphere model function in x direction used for filtering of the first embodiment of the present invention [Figure SC] A drawing for explaining response of first order partial differential of a hollow sphere model function in x direction used for correction processing of the first embodiment of the present invent ion [Figure 5Dl A drawing for explaining the response of the second order partial differential of the solid sphere in x direction corrected by the first order partial differential of the hollow sphere model function of the first embodiment of the present invention [Figure 6Al A drawing for explaining response after performing the correction processing according to the first embodiment of the present invention (case where the size of the structure corresponds to the size of the solid sphere represented by the solid sphere mode function) [Figure 6B] A drawing for explaining response after performing the correction processing according to the first embodiment of the present invention (case where the size of the solid sphere represented by the solid sphere model function is greater than the size of the structure) [Figure 71 A flowchart of processing performed in the first embodiment of the present invention [Figure 8Al Anexampleinwhichtheimageprocessingaccordingtothe first embodiment of the present invention is applied to blood vessel extraction (pseudo three-dimensional image) [Figure 8B] Anexampleinwhichtheirnageprocessingaccordingtothe first embodiment of the present invention is applied to blood vessel extraction (tomographic image) IF:igure 9A] A drawing for explaining the principle of correction processing according to asecondembodimentof the present invention [Figure 9Bl A drawing for explaining the principle of correction by first order partial differential vectors of second and third solid sphere rnodel function of the second embodiment of the present invention [BEST MODE FOR CARRYING OUT THE INVENTION] [OO261 Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. Figure 1 is a schematicblockdiagramof an image processingapparatus according to an embodiment of the present invention, illustrating a configuration thereof. The configuration of the image processing apparatus 1 shown in Figure 1 is realized by executing a program read into an auxiliary storage (not shown) on a computer Ie.g., personal computer). The program is provided being recorded on an information storage medium, such as CD-ROM and the like, or distributed via a network, such as the Internet, and installed on a computer. [OO271 The image processing apparatus 1 generates a three-dimensional image MO using a plurality of two-dimensional images captured, for example, by an X-ray CT system 2 and automatically segments a line-like structure and a plate-like structure included in the three-dimensional image MO. The image processing apparatus 1 includes an image obtaining unit 10, a detection region setting unit 20, a discrimination unit 30, a segmentation unit 40, a display unit 50, and an input unit 60. [00281 The image obtaining unit 10 obtains a plurality of CT images (two-dimensional images) captured, for example, by the X-ray CT system 2, and generates a three-dimensional image MO from the plurality of two-dimensional images. The image obtaining unit 10 maybe a unit that obtains two-dimensional images, such as so-called MRI images, RI images, PET images, X-ray images, and the like, as well as CT images. [ 00291 The detection region setting unit 20 first makes the voxel dimensions ofthe three-dimensionalimageMOisotropic. For example, if the voxel dimensions of the three-dimensional image MO are 0.31tu-n~ 0.3mm, and0.6mrnintheXr Y, andzdirectionsofthethree-dimensional image MO respectively, they are made isotropic to (X, Y, 2 ) = (0.5, 0.5, 0.5) (mm) . [0030] The detection region setting unit 20 performs a multiple resolution transformation on the three-dimensional image MO after making the image isotropic and generates a plurality of three-dimensional multiple resolution images Msi (i=O to n) (Gaussian pyramid) as shown in Figure 2. Note that i=O represents the same resolutionas the MO and i=n represents the lowest resolution. The image is reduced by the increments of 42 and the voxel dimensions of the three-dimensional multiple resolution images Msi are (X, Y, 2) = (0.5,0.!5, 0.5), (0.7, 0.7, 0.7), 1 0 1.0, 1.0) , and so on in descending order of resolution. [0031] The discrimination unit 30 includes a filtering unit 32, a correction unit 33, and an evaluation unit 34. The filtering unit 32 performs filtering, which is identical to the filtering of the method of Non-Patent Document 2, on each of the three-dimensional rtultiple resolutionirnagesMsiusinga function representinga solid sphere to be described later (solid sphere model function) and a Gaussian kernel in order to perform Hessian analysis using a Hessian matrix (evaluation matrix). That is, a filter kernel of the same size is convoluted with each of the multiple resolution images Msi having different resolutions. The solid sphere model function is defined by the radius R of the solid sphere and "o" of the Gaussian kernel. For these, appropriatevalues are setbasedonthe knowledge acquired by preliminary analysis and the like. For the radius R of the solid sphere, a value which is at least greater than "0" of the Gaussian kernel is set. [ 00321 By convoluting the filter kernel of the same size (e.g., R=2.0 (voxels), 0=0.5(voxels)) witheachofthethree-dimensionalmultiple resolutionimagesMsi, filterkernelsofdifferentsizes areapplied, in effect, to the three-dimensional image MO, so that a point-like structure, a line-like structure (e.g., blood vessel), and a plate-like structure (e.g., cortical bone) having different sizes maybe detected. Inotherwords, functions representing solidsphere with radius R in a plurality of sizes are used, and an evaluation matrix is calculated by performing filtering using a second order partial differential matrix of a function representing each solid sphere. [0033] TheHessiananalysisusing asecondorderpartialdifferential of the solid sphere model function of Non-Patent Document 2 will be described. The Hessian matrix used for the Hessian analysis is a 3x3 matrix forthe three-dimensional image, as indicatedin Formula (1) given below. Ixs I Isz v '1 = Iys Iyy Iyz Iss = -8'1 8'1 1x3; = - &? ' Izs In: Izz I 1 ( I ) hay' COO341 Eachof the elements ofthe aforementionedHessianmatrix Ixx, ~xy, Iyy, Iyz, Izz, Izx is calculated by performing filtering (convolutionoperation) on the image dataof atarget image on second order partial differential of a hollow sphere model function f(r) and a Gaussian kernel function g (r) . [ 00351 In Non-Patent Document 2, the filtering processing is performed in Fourier space. First, the image data of a target image are Fourier transformed. Then, the Fourier transformed solid sphere model function, the Gaussian kernel function, and the second order partial differential are added up to the Fourier transformed target image (FT (image) ) . Then, by performing a reverse Fourier transform on the added-up result, the filtering result is obtained. Note that the obtained filtering result is the same as the filtering result obtained by performing a convolution operation in real space. If the Fourier transform of the solid sphere model function is taken as F ( v ) and the Fourier transform of the Gaussian kernel function is takenasG(v), theaboverelationshipmayberepresentedby Formula (2) given below. i f r < R (5) = 0{, othe rwise / [0036] where, x, y, z are the three-dimensional axes in real space, and R is the radius of the solid sphere. The polar coordinate representationofthe variable (frequency) ofthe three-dimensional Fourier space is expressed as v= (v,~+v,,~+~,as~ )i ndicated in Formula (4). [0037] With respect to each function used in Formula (2) , the Fourier transformed Gaussian kernel G (v) is shown in Formula (3) above and the solid sphere model function F(v) is shown in Formula (4) above. The solid sphere model function F(v) shown in Formula (4) may be obtained by Fourier transforming the function F(r)representing a solid sphere shown in Formula (5) . The Gaussian kernel function G(v) shown in Formula (3) is used to define the differential range of pixel values of the target image, as in Non-Patent Documents 1 and In Formula (2) , the part (2rrvx)' x (~IIv,m) x (2nvZ)" corresponds to the differential processing in Fourier space and a value corresponding to each of the elements Ixx, Ixy, Iyy, Iyz, Izz, and Izx may be calculated by assigning coefficients 1, m, and n corresponding to the respective differential directions in Formula (4) such that l+mtn = 2 (0<1, O> 0 [0041] Still further, it is known that a point-like structure has characteristics that all three eigenvalues are large. For example, eigenvalues of Formula (1) have the relationship of Fo-la (8) with a target tissue of a point-like structure. 'l"' 1 ( 8 ) h3 h,3 '>"> O" i [0042] Theref ore, line-like structureness, plane-like structureness, and point-like structureness may be discriminated from the eigenvalues, and a blood vessel region which is a line-like structure and a bone region which is a plate-like structure may be segmentedinthethree-dimensionalimageMOusingthediscrimination results. [0043] The correction section 33 in the present embodiment applies eigenvalue decomposition to the Hessian matrix calculated by the filtering unit 32 and calculates three eigenvalues Al, A*, A3 ( IAI l5lkl5lA.31 . [0044] Here, the principle of inhibiting erroneous discrimination according to the present embodiment will be described using Figures 5A, 5B, 5C, 5D and specific correction processing by the correction sectlon 33 based on the principle will be described thereafter. 100451 Figure 5A shows a solid sphere model function (dash-dot line) anda responseofthe secondorderpartial differential ( s o l i d l i n e ) of the solid sphere model function a t each x position in x direction i n (A), ahollowspheremodel function (dash-dot line) andaresponse of the f i r s t order partial differential (broken line) of the hollow sphere model function at each x position in x direction in (B) , and a solid sphere model function and a response of the second order partial differential of the solid sphere model function at each x position in x direction corrected using the f i r s t order p a r t i a l differential of the solid sphere model function in ( C ) . [0046] As illustrated in Figure 5A (A), the second order p a r t i a l differential of the solid sphere model function in each direction shows response waveforms at two separate positions corresponding to the surface of the solid sphere. If a line segment traversing a structure, such as the diameter of a blood vessel or the like, corresponds to the diameter of the solid sphere represented by the solid sphere model function, two opposite portions of the contour of a structure (both ends of a l i n e segment traversingthe structure) in an image correspond respectively to the two positions where the aforementioned response waveforms of the second order partial differential of the solid sphere model function are indicated in eachdifferentialdirectionandlargeresponses (expectedresponses) maybeobtained. Thus, accordingtotheHessiananalysisofthemethod of Non-Patent Document 2, a structure, such as a blood vessel and the like, may be discriminated. [ 0047 1 In themeantime, ifonlyonepositionofthe responsewaveform of the second order partial differential of the solid sphere model function in each differential direction corresponds to a contour portion of a structure larger in radius of curvature than the solid sphere in an image, a response of a given magnitude corresponding to the response of the one position can be obtained. The present inventors have presumed that it is a cause of the erroneous ciiscriminationofa structurehavingsubstantiallythe samediameter as the diameter of the solid sphere that no distinction cannot be made between the response having a given magnitude and the expected response. Then, the present inventors have found out that the erroneous discrimination can be eliminated by cancelling out the response waveform at one position of the second order partial differential of the solid sphere model function in each direction. Then, as illustrated in Figure 3A (A), the second order partial differential of the solid sphere model function in each direction hascharacteristicsthatitshowsresponsewavefomsattwopositions symmetrical with respect to the center. Thus, the present inventors have paid attention to cancel out the response waveform at one positionofthe secondorderpartial differentialmatrixofthe solid sphere model function by the use of a function having a response waveform substantially identical in shape to the one response waveformwith a reversedpositive/negative sign at the same position as the position of the one response waveform of the second order partial differential of the solid sphere model function. LO0481 The present embodiment utilizes the fact that the response of firstorderpartialdifferentialofahollowspheremodelfunction f 1. (c) of the same size as the size of the solid sphere in x direction has characteristics that it has a response waveform having a substantially identical shape to the shape of one response waveform of the solid sphere model function with the same positive/negative sign at the same position as the position of the one of the response waveforms of the second order partial differential of the solid sphere model function in x direction and a response waveform having a substantially identical shape to the shape of the other response waveform of the solid sphere model function with a reversed positive/negative sign at the sane position as the position of the other waveformofthe second order partial differential ofthe solid sphere model function in x direction, as illustrated in Figure 5A (B), anda firstorderpart;ialdifferentialvalueofthehollowsphere model function fl (r) of the same size as the size of the solid sphere in x direction is used to cancel out the response waveform at one positionofthesecondorderpartialdifferentialofthesolidsphere rnodel in x direction. [00491 That is, addition of the response of the f i l t e r i n g using the secondorder p a r t i a l d i f f e r e n t i a l o f t h e solidspheremodel function in x direction and the response of the f i l t e r i n g using the first order p a r t i a l d i f f e r e n t i a l of the hollow sphere model function representing the hollow sphere having s u b s t a n t i a l l y t h e same radius as the radius of the solid sphere represented by the solid sphere model function w i l l r e s u l t i n that the response waveforms on the negative side in x direction are cancelled out as they have reverse signs a t the sameposition and the response waveforms on thepositive side in x direction are reinforced as they have the same sign a t the same position, and a response waveform appears only one position on the positive side i n x direction, as shown i n Figure 5A(C). [0050] Figure 5B (A) shows a solid sphere model function f (r) and (R) shows a response of the second order p a r t i a l d i f f e r e n t i a l of the solid sphere model function f (r) in x direction. Figure 5C (A) shows a hollow sphere model function fl (r) and (B) shows a response of the f i r s t order p a r t i a l d i f f e r e n t i a l of the hollow sphere model functi.onfl(r) i n x d i r e c t i o n . Figure 5Dshowsaresultoftheaddition o f t h e responseofthe secondorder p a r t i a l d i f f e r e n t i a l o f t h e solid sphere model function shown in 5B (B) and the response of the f i r s t order p a r t i a l d i f f e r e n t i a l o f t h e hollow spheremodel function fl(r) shown in Figure 5C. In Figures 5B to D, each response described above is shown byapluralityofx-yplan views havingdifferent z coordinate values of equal intervals, and the p l u r a l i t y of x-y plan views is arranged in descending order of z coordinate values from the top i n the v e r t i c a l direction. [0051] In the x-y plan views representing each response, the higher iwhi-ter) the brightness, the g r e a t e r t h e response in t h e p o s i t i v e direction and the darker (blacker) the brightness, the greater the response in the negative direction. The response waveform of the adjoining positive peak and negative peak located on the negative side of the center of the solid sphere shown in Figure 5B (B) and the response waveform of the adjoining negative peak and positive peak located on the negative side of the center of the solid sphere shown in Figure 5C (B) mutually cancel out, and it is known that no response waveform appears on the negative side of the center of the solid sphere in Figure SD. Likewise, the response waveform on the negative side of the center of the solid sphere may be cancelled out in each direction. [0052] In the present invention, the correction unit 33 corrects eigenvalues of the Hessian matrix using a first order partial differential vectors of the hollow sphere model function such that the response waveform at one position of the solid sphere model function f (r) in each direction is cancelled out based on the aforementioned principle. A specific correction method will be described hereinafter. [0053] The second order partial differential matrix and the first order partial differential vector ofthe solid spheremodel function on the aforementioned image, in the present embodiment, the correction section 33 first calculates first order partial differential vectors to be used for correction using Formula (9). More specifically, as shown in Formula (9), a Fourier transformed Gaussian kernel functionG(v) anda first order partial differential filter of a Fourier transformed hollow sphere mode function Fl(v) shown in Formula (11) are convoluted with a processing target pixel of a Fourier transformed three-dimensional multiple resolution images Msi, and the first order partial differential vectors to be used for the eigenvalue correction of the Hessian matrix are calculated by performing reverse Fourier transform of the filtering result. Here, the hollow spheremodel function f l ( v ) usedin Formula i l l ) may be obtained by performing Fourier transform on the hollow sphere model function f (r) defined by the delta function 6 (r-R4) represented by Formula (10) . f, (s) = 6(r - R,) r = J m [0054] In Formula (9) , the part (Znv,) ' x (Znv,) "x (2nvz)" corresponds to the differential processing in Fourier space and a value corresponding to each of the elements pl, p2, p3 of the first order partial differential vectors may be calculated by assigning coefficients 1, m, n corresponding to the respective differential directions in Formula (9) such that L+m+n = 1 (0<1, OCm, O