Sony Patent | Information Processing Apparatus And Surface Roughness Acquisition Method

Patent: Information Processing Apparatus And Surface Roughness Acquisition Method

Publication Number: 20200393689

Publication Date: 20201217

Applicants: Sony

Abstract

An information processing apparatus determines a plurality of sampling points in a range of a target object’s silhouette having different specular reflectances in polarization images in a plurality of azimuths, extracts polarization luminance at the sampling points in question, and derives change in luminance relative to the polarization azimuth, thus acquiring, as a phase angle, the azimuth that provides the highest luminance. Then, the information processing apparatus evaluates a characteristic of the change in phase angle relative to the change in the specular reflectance, thus identifying a subject’s surface roughness. Further, the information processing apparatus generates data to be output by performing a process according to the surface roughness and outputs the generated data.

TECHNICAL FIELD

[0001] The present invention relates to an information processing apparatus and a target object acquisition method for recognizing states of a target object and a subject space by using a captured image.

BACKGROUND ART

[0002] There are known games that use a display image obtained by capturing part of a user’s body such as the head with a video camera, extracting a given region such as the eyes, the mouth, or the hands, and replacing the region with another image (refer, for example, to PTL 1). Also known is a user interface system that receives mouth or hand motion captured with a video camera as an application’s operation instruction. As described above, techniques for capturing a real world and detecting a target object’s state and performing information processing tasks on the basis thereof have been already applied to a wide range of fields including a monitoring camera, an autonomous driving system, an inspection apparatus in manufacturing line, and an automatically controlled robot in addition to electric content.

CITATION LIST

Patent Literature

[0003] [PTL 1] EP 0999518** A**

SUMMARY

Technical Problems

[0004] A manner of a subject’s silhouette in a captured image may change in accordance with a light condition such as surrounding brightness and presence or absence of an object. For example, even in the case of capturing the same subject, a color or luminance distribution of the silhouette thereof may change significantly, or it may be difficult to recognize a shape of the subject as a result that a clear contour of the subject cannot be obtained. There are cases in which, because of the same principle, it may be difficult to distinguish whether a silhouette of a certain target object represents an original color and shape which belong to the target object or the appearance thereof is accidentally obtained according to an amount of lighting. This may cause a target object to be erroneously recognized, resulting in deteriorated accuracy for subsequent information processing. Therefore, techniques are desired that permit more accurate recognition of the state of the target object by use of a captured image.

[0005] The present invention has been devised in light of the foregoing problems, and it is an object of the present invention to provide a technique for acquiring a state of a target object with high accuracy by use of a captured image.

Solution to Problems

[0006] A mode of the present invention relates to an information processing apparatus. This information processing apparatus includes an image acquisition section adapted to acquire data of polarization images in a plurality of azimuths, a phase angle acquisition section adapted to not only derive change in polarization luminance representing a subject’s silhouette relative to the azimuth by using the polarization images but also acquire the azimuth that provides a maximum value of the polarization luminance as a phase angle, a surface roughness acquisition section adapted to acquire surface roughness of the subject by evaluating a characteristic of the phase angle with respect to change in the specular reflectance in accordance with a given reference, and an output data generation section adapted to generate data according to the surface roughness and output the generated data.

[0007] Another mode of the present invention is a surface roughness acquisition method. This surface roughness acquisition method includes a step of acquiring data of polarization images in a plurality of azimuths, a step of not only deriving change in polarization luminance representing a subject’s silhouette relative to the azimuth by using the polarization images but also acquiring the azimuth that provides a maximum value of the polarization luminance as a phase angle, a step of acquiring surface roughness of the subject by evaluating a characteristic of the phase angle with respect to change in the specular reflectance in accordance with a given reference, and a step of generating data according to the surface roughness and outputting the generated data.

[0008] It should be noted that any combinations of the above components and conversions of expressions of the present invention between a method, an apparatus, and the like are also effective as modes of the present invention.

Advantageous Effect of Invention

[0009] According to the present invention, it is possible to acquire a state of a target object with high accuracy by use of a captured image.

BRIEF DESCRIPTION OF DRAWINGS

[0010] FIG. 1 is a diagram illustrating a configuration example of an information processing system in the present embodiment.

[0011] FIG. 2 depicts diagrams each illustrating a spherical silhouette of a subject in the present embodiment.

[0012] FIG. 3 is a diagram schematically illustrating a capturing environment of polarization images used in the present embodiment.

[0013] FIG. 4 is a diagram comparing change in polarization direction relative to an incident angle between specular reflection and diffuse reflection.

[0014] FIG. 5 is a diagram for describing definitions of parameters used in the present embodiment.

[0015] FIG. 6 is a diagram illustrating change in luminance relative to a polarization azimuth in the present embodiment.

[0016] FIG. 7 is a diagram illustrating results of change in phase angle acquired from an actual captured image in the present embodiment.

[0017] FIG. 8 depicts diagrams each illustrating a relationship between a transmission axis angle and luminance on the assumption that only s polarized light is observed in the present embodiment.

[0018] FIG. 9 depicts diagrams each illustrating a relationship between the transmission axis angle and the luminance in the case where p polarized light is mixed in light observed in the assumption made in FIG. 8.

[0019] FIG. 10 is a diagram illustrating a relationship in magnitude between the s polarized light and the p polarized light included in the observed light and correspondence with the relationship between the transmission axis angle and the luminance, in the present embodiment.

[0020] FIG. 11 is a diagram illustrating results of simulation of the change in luminance relative to the transmission axis angle when orientations of the p polarized light and the s polarized light are out of alignment with the x and y axes, respectively, in the present embodiment.

[0021] FIG. 12 is a diagram illustrating a manner in which surface roughness and a polarization state are modeled in the present embodiment.

[0022] FIG. 13 is a diagram for describing a relationship between normal vector directions of minute planes and the phase angle when the normal vector direction has a normal distribution in the present embodiment.

[0023] FIG. 14 is a diagram illustrating results of simulation of the change in phase angle relative to the specular reflectance when a subject surface is modeled as a set of minute planes having different normal directions in the present embodiment.

[0024] FIG. 15 is a diagram illustrating the change in phase angle relative to the specular reflectance when a diffuse reflectance is changed in the present embodiment.

[0025] FIG. 16 is a diagram illustrating the change in phase angle relative to the specular reflectance when a ratio between the s polarized light and the p polarized light in specular reflected light is changed in the present embodiment.

[0026] FIG. 17 is a diagram illustrating an internal circuit configuration of an information processing apparatus in the present embodiment.

[0027] FIG. 18 is a diagram illustrating a functional block configuration of the information processing apparatus in the present embodiment.

[0028] FIG. 19 is a diagram illustrating a structural example of an imaging device having a polarizer layer that can be introduced into an imaging apparatus in the present embodiment.

[0029] FIG. 20 is a diagram illustrating a relationship between a subject surface position and a specular reflectance in the present embodiment.

[0030] FIG. 21 is a diagram illustrating a relationship between a surface position of a subject having a different shape from that of FIG. 20 and a specular reflectance in the present embodiment.

[0031] FIG. 22 depicts diagrams each schematically illustrating a manner in which the phase angle is expressed as a function of the position in the capturing environment as illustrated in FIGS. 20 and 21.

[0032] FIG. 23 depicts diagrams illustrating the change in the phase angle relative to the specular reflectance and an example of drawing an object having the corresponding surface roughness in the present embodiment.

[0033] FIG. 24 is a flowchart illustrating a processing procedure for the information processing apparatus to acquire information including the surface roughness of the target object from a captured image and output necessary data in the present embodiment.

DESCRIPTION OF EMBODIMENT

[0034] FIG. 1 illustrates a configuration example of an information processing system in the present embodiment. This information processing system includes an imaging apparatus 12, an information processing apparatus 10, and a display apparatus 16. The imaging apparatus 12 captures an image of a subject 8. The information processing apparatus 10 acquires data of the captured image and performs a given information processing task. The display apparatus 16 outputs a result of the information processing. The information processing system may further include an input apparatus that accepts operation on the information processing apparatus 10 from a user. The information processing apparatus 10 may further be capable of communicating with an external apparatus such as a server by connecting to a network such as the Internet.

[0035] The information processing apparatus 10, the imaging apparatus 12, and the display apparatus 16 may be connected by cables or wirelessly by wireless LAN (Local Area Network) or the like. Also, two or more of the information processing apparatus 10, the imaging apparatus 12, and the display apparatus 16 may be combined into an integral apparatus. For example, an information processing system may be realized by using a camera or a mobile terminal having these apparatuses. Alternatively, a head-mounted display that is worn on the user’s head and displays an image in front of the user’s eyes may be used as the display apparatus 16, and the imaging apparatus 12 may be provided on the head-mounted display in such a manner as to capture an image corresponding to a user’s line of sight. In any case, the information processing apparatus 10, the imaging apparatus 12, and the display apparatus 16 are not limited to those illustrated in appearance and shape.

[0036] In such a system, the information processing apparatus 10 successively acquires image data captured by the imaging apparatus 12 and performs image analysis including identification of the subject’s surface roughness, and then performs information processing on the basis of a result of the image analysis, generating a display image data and audio data to output the generated image data and audio data to the display apparatus 16. Here, the details of information processing performed by the information processing apparatus 10 as a result of image analysis are not specifically limited. For example, a game controller may be a given target object included in the subject 8 so that an electronic game or an arbitrary information processing task is progressed by recognizing the motion of the game controller as user operation.

[0037] Alternatively, the controller may be replaced with a virtual object in the captured image for use as a display image, or a virtual object that interacts with the subject may be drawn. A virtual world drawn in a field of view corresponding to the user’s line of sight may be displayed on the head-mounted display by modeling the real world as a virtual object.

[0038] It is preferred that such a technique should identify the subject 8 and its surrounding conditions as accurately as possible. For example, in a case where another object similar in shape to the target object exists in the subject space, it is necessary to discriminately recognize silhouettes thereof. However, the manner in which a silhouette appears and the ease with which the silhouette can be extracted from a captured image change depending on various factors including surrounding brightness, light source condition, color of the target object, pattern, and shape. Therefore, it is considered that a simple process based on a common captured image does not provide constant accuracy.

[0039] FIG. 2 illustrates spherical silhouettes of the subject 8. The silhouette in (a) has a locally high luminance at the center of the spherical silhouette. Such an image is acquired, for example, in a case where light having relatively high directivity is emitted from the front side in the figure on a sphere including a material that readily produces specular reflection. That is, it is considered that specular reflection is predominant at the center of the sphere and that diffuse reflection is predominant at portions near a contour. In this case, specular reflection is light emitted from a light source and regularly reflected on the subject surface whereas diffuse reflection is light that appears on the surface after having reached the inside of the subject and having been diffused by pigment particles. According to a dichroic reflection model, light observed by the imaging apparatus 12 is expressed, of these reflected light beams, as the sum of components in a direction of an imaging surface.

[0040] In contrast, the silhouette in (b) has lower luminance at the center portion than that of (a) with a mild change in luminance toward the outline. The silhouette in (c) has even lower luminance at the center portion, depicting no significant difference in luminance from the portions near the contour. The changes of the silhouettes in (b) and (c) relative to the silhouette in (a) may occur as a result of an increase in area of the light source. Meanwhile, a similar change also occurs as a result of an increase in surface roughness of the sphere. Here, the term “roughness” refers to variation in height or surface azimuth attributable to projections and depressions of substantially several micrometers on an object surface. It is assumed that the larger the variation, the greater the roughness. The surface roughness is a common parameter in material processing technology and other fields.

[0041] If it is impossible to distinguish whether the difference between the silhouettes as illustrated is attributable to the light source or the subject itself, it is probable that the same subject may be recognized as different objects because of the change of the light source and that another object having different surface roughness may be mistaken for the target object. Also, it is difficult to distinguish between whether specular reflected light is scattered on the surface due to a rough surface or light is scattered inside by a material that readily produces diffuse reflection. For this reason, problems may occur also in the case of distinguishing between the target object silhouettes by material and in the case of drawing a virtual object corresponding to a real object by applying a reflection model. Particularly, in a case where the target object or the imaging surface moves, the appearance changes successively due to the change in the state of reflected light, thus providing an effect that cannot be ignored also on the accuracy of subsequent processes. For this reason, the present embodiment identifies the surface roughness of a subject as a parameter that remains unaffected by the state of light by using polarization images.

[0042] FIG. 3 schematically illustrates a capturing environment of polarization images used in the present embodiment. The imaging apparatus 12 captures an image of a space including a subject 72 via a linear polarizer plate 70. In more details, the imaging apparatus 12 observes, of reflected light that includes a specular reflection component obtained as a result of causing light emitted from a light source 74 to be reflected on the light by the subject 72 and a diffuse reflection component obtained as a result of causing the light emitted from a light source 74 to be scattered inside the subject 72, polarized light that oscillates in a direction determined by the linear polarizer plate 70. In the case of specular reflection, an angle .theta. formed between a normal vector n at an observation point a on the surface of the subject 72 and a light beam reaching the point a from the light source 74 is referred to as an incident angle, and a plane 76 including the light beam and the normal vector n is referred to as an incident plane. In the case of diffuse reflection, an angle .theta.’ formed between the light beam reaching the point a from inside the subject 72 and the normal vector n is the incident angle, and the plane 76 including the light beam and the normal vector n is the incident plane.

[0043] The linear polarizer plate 70 transmits, of reflected light that reaches the imaging apparatus 12 from the observation point a, only linear polarized light oscillating in a certain direction. Hereinafter, the oscillation direction of polarized light that passes through the linear polarizer plate 70 will be referred to as a transmission axis of the linear polarizer plate 70. The rotation of the linear polarizer plate 70 about an axis vertical to its surface allows for the transmission axis to be set up in an arbitrary direction. Assuming that light that reaches the imaging apparatus 12 is non-polarized light, observed luminance is constant even if the linear polarizer plate 70 is rotated. Meanwhile, when partially polarized, common reflected light experiences change in luminance observed in the transmission axis direction. Also, the luminance changes in different ways depending on a ratio between specular reflection and diffuse reflection and the incident angle.

[0044] FIG. 4 compares change in polarization direction relative to an incident angle between specular reflection and diffuse reflection. Here, the term “s polarized light” refers to a component that oscillates in a direction vertical to the incident plane, and the term “p polarized light” refers to a component that oscillates in a direction parallel to the incident plane. In both specular reflection and diffuse reflection, the ratio between the s polarized light and the p polarized light is dependent on the incident angle. Also, the s polarized light is predominant in specular reflected light regardless of the incident angle. For this reason, the observed luminance is maximum when the transmission axis of the linear polarizer plate 70 is vertical to the incident plane, and the observed luminance is minimum when the transmission axis of the linear polarizer plate 70 is parallel to the incident plane.

[0045] Diffuse reflected light is the opposite thereof. The observed luminance is maximum when the transmission axis of the linear polarizer plate 70 is parallel to the incident plane, and the observed luminance is minimum when the transmission axis of the linear polarizer plate 70 is vertical to the incident plane. Therefore, the change in luminance obtained by capturing polarization images in various directions of the transmission axis includes information regarding a contained ratio between specular reflection component and diffuse reflection component and incident angle. The present embodiment also takes advantage of such a change in luminance of polarized light.

[0046] FIG. 5 is a diagram for describing definitions of parameters used in the present embodiment. As in FIG. 3, a silhouette of the observation point a is formed at a position b on a virtual image plane 80 by a light beam 82 that reaches the imaging apparatus 12 from the observation point a on the subject 72 through the linear polarizer plate 70. Here, as illustrated on the image plane 80, the position b where an image is formed is assumed to be an origin, and the horizontal rightward direction as seen from the imaging apparatus 12 is denoted as an x axis, the vertical upward direction is denoted as a y axis, and the angle formed between the transmission axis of the linear polarizer plate 70 and the x axis is denoted as a polarization azimuth .PHI.. As described above, a behavior of luminance I observed at the position b with change in the polarization azimuth .PHI. is determined by the ratio between specular reflection component and diffuse reflection component and the incident angle .theta.. Also, the s polarized light and the p polarized light are light beams that oscillate vertically and horizontally to the incident plane 76, respectively.

[0047] FIG. 6 illustrates change in luminance I relative to the polarization azimuth .PHI.. The graph on the upper side in FIG. 6 illustrates a case where light that reaches the imaging apparatus 12 is only specular reflection, and the graph on the lower side in FIG. 6 illustrates a case where light is only diffuse reflection, and each is in a shape of a sine wave with a 180.degree. period. Meanwhile, a polarization azimuth .phi.s when the luminance I in specular reflection has a maximum value Imax differs by 90.degree. from the polarization azimuth yd when the luminance I in diffuse reflection has the maximum value Imax. This is attributable, as illustrated in FIG. 4, to the fact that the s polarized light is predominant in specular reflection and that the p polarized light is predominant in diffuse reflection. Considering the fact that the s polarized light is vertical to the incident plane and that the p polarized light is horizontal to the incident plane, the polarization azimuth (.phi.s–90.degree.) that provides the lowest luminance in specular reflection or the polarization azimuth yd that provides the highest luminance in diffuse reflection represents the angle on the image plane of the incident plane. The angle of interest is commonly referred to as an azimuth angle.

[0048] Hereinafter, the polarization azimuth that provides the maximum luminance of observed polarized light will be referred to as a phase angle .phi. regardless of the contained ratio between specular reflection and diffuse reflection. The change in the luminance I illustrated in FIG. 6 can be expressed by the following formula.

[Math. 1] I=I.sub.max+I.sub.min/2+I.sub.max-I.sub.min/2 cos(2.PHI.-2.psi.) (Formula 1)

[0049] FIG. 7 illustrates results of the change in the phase angle .phi. acquired from an actual captured image. A captured image 90 of a cylindrical subject is illustrated on the upper side in FIG. 7, and a change 94 in the phase angle .phi. on a line 92 on the image plane is illustrated on the lower side in FIG. 7. The phase angle .phi. is acquired by extracting, from a plurality of polarization images captured with different transmission axis angles, luminance of each of the pixels included in the line 92 and obtaining the change in luminance relative to the polarization azimuth as illustrated in FIG. 6.

[0050] At this time, observed luminance values are acquired only relative to discrete polarization azimuths and are therefore approximated to a function in the form of Formula 1 by using a least squares method or the like. In the captured image 90, of the subject’s silhouette, a portion indicated by an arrow is locally high in luminance, thus suggesting that specular reflection is predominant. When the azimuth angle is set to the horizontal direction (0.degree.) because of a cylindrical shape, the phase angle .phi. of specular reflected light is theoretically 90.degree., and this value is also acquired in the change 94 in the phase angle .phi. depicted on the lower side. In other portions where a diffuse reflection component is considered to be predominant, on the other hand, there is no region where the phase angle .phi. is 0.degree.. The present inventor conceived that such a change in the phase angle .phi. is brought about by not only the ratio between reflection components but also the surface roughness of the subject. A description will be given next of the principle.

[0051] FIG. 8 illustrates a relationship between the transmission axis angle and the luminance on the assumption that only the s polarized light is observed. (a) illustrates a manner in which the linear polarizer plate 70 having a transmission axis 86 is rotated about an xy plane. It should be noted that, in this figure, the azimuth angle is the y-axis direction and that the s polarized light vertical thereto oscillates in the x axis. The same is also true for the description given below. In a case where only the s polarized light reaches the imaging apparatus 12, the luminance is maximum when the transmission axis 86 is in the direction of the x axis and minimum when the transmission axis 86 is in the direction of the y axis. If this is generalized by denoting the angle of the transmission axis 86 relative to the x axis as .theta., an electric field component of the s polarized light to be incident as Es, and the electric field component that passes through the polarizer plate as E.sub.proj, the following relationship holds:

E.sub.proj=Es cos .theta.

Hence, the observed luminance I changes in the following manner relative to the angle .theta.:

I=E.sub.proj2=Es.sup.2 cos.sup.2 .theta.

[0052] (b) of FIG. 8 is a graph illustrating the normalized luminance I with a maximum value of 1.0 expressed on a two-dimensional plane with x=I cos .theta. and y=I sin .theta.. For example, when the transmission axis matches .theta.=0.degree., i.e., the x axis (y=0), the luminance I has the maximum value of 1.0, and when the transmission axis matches .theta.=90.degree., i.e., the y axis (x=0), the luminance I has the minimum value of 0. FIG. 9 illustrates a relationship between the transmission axis angle and the luminance in a case where the p polarized light is mixed in light observed in the assumption made in FIG. 8. (a) is a diagram similar to (a) of FIG. 8, and the x axis is in the oscillation direction of the s polarized light, and the angle formed between the transmission axis 86 and the x axis is denoted as .theta.. It is assumed, however, that incident light includes not only the s polarized light of an electric field component Es but also the p polarized light of an electric field component Ep. In this case, the luminance I that is observed after passing through the polarizer plate changes in the following manner relative to the angle .theta.:

I=Es.sup.2 cos.sup.2 .theta.+Ep.sup.2 sin.sup.2 .theta.

[0053] (b) of FIG. 9 illustrates the luminance I in this case in a similar form to (b) of FIG. 8. It should be noted, however, that because Es:Ep=0.8:0.2, the maximum value of the luminance I is 0.8. The comparison demonstrates that the case in FIG. 9 differs from that in FIG. 8 in that when the transmission axis matches .theta.=90.degree., i.e., the y axis (x=0), the luminance I is not 0 due to the presence of the p polarized light. In contrast, the luminance I is maximum when the transmission axis matches .theta.=0.degree., i.e., the x axis (y=0), as in the case illustrated in FIG. 8. That is, in a case where the s polarized light is predominant as in specular reflection, the angle that provides the maximum luminance, i.e., the phase angle .phi., remains unchanged at 0.degree. even if the p polarized light is mixed.

[0054] FIG. 10 illustrates a relationship in magnitude between the s polarized light and the p polarized light included in the observed light and correspondence with the relationship between the transmission axis angle and the luminance. The graph on the left depicts change in luminance when the s polarized light is greater than the p polarized light and corresponds to (b) of FIG. 9. The graph at the center depicts the change in luminance when the s polarized light is equal in ratio to the p polarized light, and the graph on the right depicts the change in luminance when the p polarized light is greater than the s polarized light. As described above, when the s polarized light is larger in ratio, the phase angle .phi.=0.degree.. Conversely, when the ratio is reversed, the phase angle .phi.=90.degree.. That is, according to the above theory, the phase angle .phi. is either 0.degree. or 90.degree. with a boundary point at the state where the s polarized light and the p polarized light are equal in ratio and does not have any intermediate value.

[0055] It should be noted that, for the phase angle .phi. here, the s polarized light oscillates in the direction of the x axis. Meanwhile, the phase angle .phi. changes mildly in actual measurements illustrated in FIG. 7. A subject surface roughness parameter is introduced to explain this phenomenon. That is, in the example described so far, it has been assumed that a specular reflection component is reflected uniformly toward a regular reflection direction from incident light as illustrated in FIG. 5. In contrast, in a case where the surface is rough, that is, there are minute projections and depressions on the surface, the orientation of the normal vector changes from one minute area to another. As a result, a specular reflection component is not reflected in a uniform direction, and the reflection direction has, instead, a distribution.

[0056] For this reason, even if the s polarized light is oriented, as a whole surface, in the azimuth angle of the subject in such a manner as to match the x axis as has been described so far, there may be a case where the orientation of the s polarized light may be misaligned with the x axis when inspected in detail with micrometer levels. FIG. 11 is a diagram illustrating results of simulation of the change in luminance relative to the transmission axis angle when the orientations of the p polarized light and the s polarized light are out of alignment with the x and y axes, respectively. It should be noted, however, that Es:Ep=0.8:0.2. The upper side of FIG. 11 illustrates a manner in which the linear polarizer plate 70 having the transmission axis 86 is rotated about the xy plane similarly to (a) of FIG. 8. Here, the azimuth angle, i.e., the angle of the oscillation direction of the p polarized light relative to the y axis, is denoted as .alpha. as illustrated.

[0057] Of the change in luminance illustrated on the lower side, the oscillation direction of the s polarized light matches the x axis when .alpha.=0.degree. illustrated on the left. This is nothing but the example illustrated in (b) of FIG. 9. Therefore, the luminance has the maximum value when the transmission axis 86 matches the x axis. That is, the phase angle .phi.=0.degree.. In contrast, when .alpha.=90.degree. illustrated on the right, the oscillation direction of the s polarized light matches the y axis. For this reason, the luminance has the maximum value when the transmission axis 86 matches the y axis. It should be noted that this situation is, as a result, the same as the condition on the right in FIG. 10 in which the s polarized light is mixed with the p polarized light that oscillates in the direction of the y axis to a certain degree. In this case, the phase angle satisfies the relation .phi.=90.degree..

[0058] Also, in a case where the relation .alpha.=30.degree. or 60.degree. is satisfied, the transmission axis that provides the maximum luminance has an inclination equivalent to that amount relative to the x axis. In a case where the azimuth angle .alpha. is defined relative to the y axis as illustrated, the phase angle .phi. of light with a high ratio of the s polarized light relative to the x axis is equal to the azimuth angle .alpha.. Because the azimuth angle is dependent on the orientation of the normal vector on the subject surface, it can be said that the phase angle .phi., as a result, changes dependently on the normal vector. FIG. 12 illustrates a manner in which surface roughness and a polarization state are modeled. In a case where there are minute projections and depressions on the subject surface as illustrated, light observed by the imaging apparatus 12 through the linear polarizer plate 70 is a superposition of reflected light beams from minute planes 96 having different normal directions.

[0059] Therefore, the phase of polarized light is also a superposition of these reflected light beams. FIG. 13 is a diagram for describing a relationship between normal vector directions of minute planes and the phase angle .phi. when the normal vector directions have a normal distribution. Assuming, in FIG. 13, that the center value of the s polarized light is 0.degree., if the normal vector direction has a normal distribution, the azimuth of the s polarized light also has a normal distribution around 0.degree.. Also, the azimuth of the p polarized light has a normal distribution around 90.degree.. In a case where specular reflection is predominant, the s polarized light is significantly higher in ratio than the p polarized light as illustrated. Therefore, the superposition thereof also provides the maximum 0.degree. polarization azimuth component. As a result, the phase angle .phi. is 0.degree..

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