JP7016646B2 - Image processing equipment, image processing methods and programs - Google Patents

Description

The present invention relates to an image processing technique for the gloss of an object in an image.

Conventionally, a technique for adding gloss to an object in an image has been known. Patent Document 1 discloses, in 3D computer graphics (3DCG), a technique for adding a highlight to an arbitrary position in an object to be rendered by setting a light source position so that specularly reflected light faces a viewpoint. ing. In this technique, highlights are added by designating an arbitrary range of an object and setting the light source position so that the reflected light in that range becomes specularly reflected light.

On the other hand, a technique for reproducing fine uneven shapes on the surface of an object by CG or the like has begun to spread. An object having a fine uneven shape on the surface has a finer change in the normal direction of the reflecting surface according to a change in the uneven shape, as compared with an object having a smooth surface. This fine change in the normal direction gives a fine change in the specular reflection direction of the light and, by extension, the intensity of the reflected light observed from the viewpoint position. This fluctuation appears as a texture peculiar to the object. For example, it is known that the above-mentioned texture appears in a metallic material containing minute metal flakes, a material subjected to satin finish, and the like.

Japanese Unexamined Patent Publication No. 6-111028

When an attempt is made to add a highlight to an object that attempts to reproduce the texture of a metallic material or the like as described above using the technique disclosed in Patent Document 1, the reflected light at the highlight portion is uniformly specularly reflected as described above. It becomes light. Therefore, the fine variation in the intensity of the reflected light described above does not occur in the highlight portion. As a result, there is a problem that the texture peculiar to the object in the highlight portion is impaired.

The present invention has been made in view of the above problems, and an object of the present invention is to provide a process for enhancing the gloss of an object in consideration of the shape of the surface of the object.

In order to solve the above problems, the image processing apparatus according to the present invention looks at the object and the first acquisition means for acquiring the shape information representing the shape of the object surface and the reflection characteristic information representing the reflection characteristic of the object. The object is obtained based on the second acquisition means for acquiring the viewpoint information regarding the viewpoint and the light source information regarding the light source that illuminates the object, the reflection characteristic information, the viewpoint information, the light source information, and the shape information. In the image data to be represented, the enhancing means for emphasizing the light reflection intensity of the object and the object for which the light reflection intensity is emphasized by the enhancing means are provided so that the higher the flatness of the shape is, the higher the emphasizing degree is. It has an output means for outputting the image data to be represented, and is characterized in that the degree of flatness of the shape is a degree of flatness of a global shape different from the fine uneven shape of the surface of the object .

According to the present invention, the gloss of the object can be emphasized in consideration of the shape of the surface of the object.

The figure which shows the hardware composition of the image processing apparatus 100 Block diagram showing the functional configuration of the image processing device 100 A flowchart showing the flow of a series of processes in the image processing device 100. Flow chart showing the flow of processing in the generation unit 204 Diagram showing an example of shape features The figure which shows an example of a feature image Diagram showing an example of a base image A diagram showing an example of an output image Diagram showing an example of reflection

Hereinafter, embodiments for carrying out the present invention will be described with reference to the drawings.

[Embodiment 1]
In the present embodiment, a process of changing the degree of emphasis for emphasizing gloss is performed according to the characteristics of the shape of the surface of the object to be rendered. This will be described in detail below.

<Hardware configuration of image processing device 100>
FIG. 1 is a diagram showing a hardware configuration example of the image processing device 100. The image processing device 100 includes a CPU 101, a ROM 102, a RAM 103, a hard disk drive (HDD) 104, an HDD interface (I / F) 105, an input I / F 106, an output I / F 107, and a system bus 108. The CPU 101 uses the RAM 103 as a work memory to execute programs stored in the ROM 102 and the HDD 104, and controls each part described later via the system bus 108. The HDDI / F105 is an interface such as Serial ATA (SATA) for connecting a secondary storage device such as an HDD104 or an optical disk drive. The CPU 101 can read data from the HDD 104 and write data to the HDD 104 via the HDDI / F105. Further, the CPU 101 can expand the data stored in the HDD 104 into the RAM 103, and similarly, can store the data expanded in the RAM 103 in the HDD 104. Then, the CPU 101 can regard the data expanded in the RAM 103 as a program and execute it. The input I / F 106 is a serial bus interface such as USB for connecting an input device 109 such as a keyboard, a mouse, and a 3D scanner. The CPU 101 can read various data from the input device 109 via the input I / F 106. The output I / F 107 is a serial bus interface such as USB or IEEE that connects an output device 110 such as a monitor or a printer. The CPU 101 can send data to the output device 110 via the output I / F 107 to execute display and recording. If a bidirectional communication interface such as USB or IEEE is used, the input I / F 106 and the output I / F 107 can be combined into one.

<Functional configuration of image processing device 100>
FIG. 2 is a block diagram showing a functional configuration of the image processing apparatus 100. The image processing device 100 has a first acquisition unit 201, a second acquisition unit 202, a calculation unit 203, and a generation unit 204.

The first acquisition unit 201 acquires object data including object shape information and reflection characteristic information from an input device 109 or a database (not shown). Here, the shape information is data representing the shape of the object surface, and is used as mesh data in the present embodiment. The mesh data is data necessary for displaying a mesh model that expresses the shape of an object by a set of plate-shaped elements having a plurality of sides. For example, the coordinate data and the normal vector of each vertex of the triangle arranged in the three-dimensional space. The data format of the shape information may be any one that can specify the position and shape of the object, and may be, for example, a parametric model represented by a NURBS curved surface or the like. Further, the reflection characteristic information is data representing the reflection characteristic of the object. The reflection characteristic information in the present embodiment includes the diffuse reflectance coefficient kd, the ambient light reflection coefficient ka, the mirror surface reflection coefficient ks, and the mirror surface reflection index n in the mirror surface reflection model of the phone represented by the following equations (1) to (5). do.
I = I _Dr + I _Ar + I _Sr ... Equation (1)
I _Dr = I _Di × k _d × (N ・ L) ・ ・ ・ Equation (2) I _Ar = I _Ai × _ka・ ・ ・ Equation (3)
I _Sr = I _Si × k _s × (L ・ R) ⁿ ... equation (4) R = −E + 2 (NE) N ・ ・ ・ equation (5)

Here, I is the intensity of the reflected light with respect to the incident light and the ambient light from the light source incident on the object, and I _Dr is the diffuse reflection component (intensity of the diffuse reflected light) of I. Further, I _Ar is an ambient light component of I (intensity of reflected light with respect to the ambient light incident on the object), _ISr is a specular reflection component of I (intensity of specular reflected light), and R is a reflection vector. Further, _IDi is the intensity of incident light from a light source that contributes to diffuse reflection in the object, and _IAi is the intensity of ambient light incident on the object. Further, _ISi is the intensity of incident light from a light source that contributes to specular reflection in an object, and N, L, and E are a normal vector, a light source vector, and a line-of-sight vector, respectively. The parameters of other reflection models such as the specular reflection model of Brin-Fon may be used as the reflection characteristic information. The acquired object data is sent to the calculation unit 203 and the generation unit 204.

The second acquisition unit 202 acquires rendering parameters including viewpoint information and light source information used for rendering the object by a user instruction via the input I / F 106. In addition, you may acquire what was stored in the storage device such as HDD 104 in advance. The viewpoint information is the position of the viewpoint, the direction of the line of sight from the viewpoint, and the range (angle of view) seen from the viewpoint. The light source information is the position of the light source, the direction in which the light is directed from the light source (light ray direction), and the intensity of the light emitted by the light source. The acquired rendering parameters are sent to the calculation unit 203 and the generation unit 204.

The calculation unit 203 calculates a shape feature amount representing the shape feature of the object surface based on the object data and the rendering parameter. Details will be described later. The calculated shape feature amount is sent to the generation unit 204.

The generation unit 204 includes a feature image generation unit 205, a base image generation unit 206, and a composition unit 207. The generation unit 204 generates and outputs an output image representing an object whose gloss is emphasized according to the shape feature amount. One of the factors that give the texture of an object is the fluctuation of the reflection intensity based on the spatial distribution in the normal direction of the reflection surface. In this embodiment, a specular reflection model of a phone, which is a widely used reflection model, is assumed, and the texture of the object is emphasized by emphasizing the specular reflection component (gloss) in which the change in the normal direction greatly contributes to the intensity. Generates an output image that emphasizes. In addition, in a flat surface portion where the angle between the incident direction and the line-of-sight direction of the light between the neighboring meshes is gradual and uneven, the fluctuation range of the reflected light intensity becomes smaller and the texture becomes smaller. Becomes difficult to understand. Therefore, in this embodiment, the closer the shape of the object is to a flat surface, the higher the degree of emphasis on gloss. FIG. 9 shows an example of reflection. The object 901 in FIG. 9A represents a flat plate-like object having fine irregularities on its surface. Further, the object 911 in FIG. 9B represents a curved object having fine irregularities on the surface. When the object is irradiated from the light source 902, each of the light rays 903 is reflected at a point on the object 901. The reflected light ray 905 is incident on the viewpoint 904. The alternate long and short dash line 906 schematically represents specular reflection when light is incident from the light ray 903 from the light source direction on a small region including fine irregularities on the object 901. Usually, specular reflection refers to reflection in one direction in which the incident angle and the reflection angle of light are the same with respect to the reflecting surface. However, considering a small region including fine irregularities on the surface of the object, specular reflection in the small region appears to occur in various directions according to the normal of the fine irregularities. That is, the specular reflection direction seems to have a spread, and this spread appears as a texture. In a general metallic material, the reflected light directed to the specular reflection direction is the strongest when the approximate plane of a small region is used as the reflection surface. Therefore, when the specular reflection direction and the line-of-sight direction of the approximate plane are different, the observed specular reflected light is relatively weak. The curve 908 of FIG. 9A schematically represents the intensity of the specular reflection component from each point on the object 901 toward the line of sight. In the example of FIG. 9A, since there is no reflection point on the object 901 where the specular reflection direction and the line-of-sight direction of the approximate plane coincide with each other, the maximum intensity of the reflected light observed at the viewpoint position is reduced. On the other hand, the curve 918 of FIG. 9B shows the intensity of the specular reflection component from each point on the curved object 911 toward the line of sight. In general, the position conditions of the viewpoint and the light source from which the specularly reflected light of a certain surface is obtained are limited to a narrow range based on the normal direction of the surface. Therefore, it is more difficult to obtain strong specular reflection and the texture is difficult to understand for an object close to a plane whose normal direction is oriented in a certain direction than for a curved object whose normal direction is oriented in various directions.

Hereinafter, each part constituting the generation part 204 will be described. The details of the processing in each part will be described later.

The feature image generation unit 205 obtains a specular reflection component of an object of incident light from a light source, and performs enhancement processing according to the shape feature amount to generate feature image data. The generated feature image data is sent to the synthesis unit 207.

The base image generation unit 206 obtains the diffuse reflection component in the object of the incident light from the light source and the intensity of the reflected light in the object of the ambient light, and generates the base image data. The generated base image data is sent to the compositing unit 207.

The synthesizing unit 207 synthesizes the feature image data and the base image data to generate output image data.

<Processes executed by the image processing device 100>
FIG. 3 is a flowchart showing an operation procedure of a series of processes in the image processing apparatus 100. This series of processes is realized by reading a computer-executable program describing the procedure shown below from the ROM 102 or the HDD 104 onto the RAM 103, and then executing the program by the CPU 101. Hereinafter, each step (process) is represented by adding S in front of the reference numeral.

In S301, the first acquisition unit 201 acquires object data. The second acquisition unit 202 acquires rendering parameters. In S302, the calculation unit 203 calculates the shape feature amount based on the object data acquired in S301 and the rendering parameter. In the present embodiment, the planes constituting the outline of the object are obtained based on the normals of the surface of the object, and the degree of variation (dispersion) in the normal direction in each plane is calculated as the shape feature amount. Here, the faces that make up the outline of the object are adjacent to each other whose normal vectors are similar when the object is viewed from a global perspective (that is, when the fine irregularities on the surface are ignored). It is a set of meshes. The details of the process for calculating the shape feature amount are shown below.

First, based on the object data and the rendering parameters, a normal image is generated in which the normal vector of the mesh constituting the object included in the angle of view of the rendering is recorded as a pixel value. In the present embodiment, the vertex coordinates (x, y, z) of the mesh in the three-dimensional space are set to the pixel positions (i, j) on the two-dimensional image by using the formula (6) which is a general projection conversion formula. Convert to. The normal vector (nx, ny, nz) corresponding to this vertex is recorded as the pixel value N (i, j) of the pixel (i, j).

Here, M _s , M _p , and M _v are a screen transformation matrix, a projective transformation matrix, and a view transformation matrix determined from the rendering parameters, respectively. For the pixels corresponding to the inside of the mesh, the values interpolated from the normal vector corresponding to each vertex constituting the mesh are stored. Since a known rendering process in computer graphics can be used for generating the normal image (a two-dimensional image in which a pixel value N (i, j) is recorded in each pixel) described above, a detailed description thereof will be given. Is omitted.

Next, the generated normal image is subjected to a smoothing process to generate a smoothed normal image in which fluctuations in the normal due to fine irregularities are removed, and the smoothed normal image is divided into regions. A known Gaussian filter is used for smoothing. Let the pixel value of the smoothed normal image be N'(i, j). A moving average filter, a median filter, or the like may be used for smoothing. Further, a known region growth method is used for region division. In addition, other known methods such as threshold processing based on a histogram may be used. Each region obtained by the region division is a region in which the normal vector points in substantially the same direction, and thus can be regarded as a surface constituting the outline of the object.

Next, for each pixel (i, j) of the smoothed normal image, the shape feature amount F (i, j) is calculated according to the equations (7) and (8).

Here, R _k is a region including pixels (i, j) in the region obtained by region division, and num (R _k ) is the number of pixels in the region R _k . Further, θ (i, j) represents the angle formed by the smoothed normal vector N'(i, j) and the predetermined reference vector N ₀ (for example, (1, 0, 0)). The shape feature amount F (i, _j ) in the equation (7) corresponds to the dispersion of the direction of the smoothed normal vector N'(i, j) in the region Rk including the pixel (i, j). Then, the closer the surface of the object corresponding to the region to which the pixel (i, j) belongs to the plane, the closer the value approaches zero. The area-divided normal image of the object shown in FIG. 5 (a) is shown in FIG. 5 (b), and the figure showing the shape feature amount as the brightness is shown in FIG. 5 (c). In the example of this figure, the rectangular parallelepiped 501 having a flat surface has a small amount of shape features, and the sphere 502 having a curved surface has a large amount of shape features. By the above processing, the shape feature amount F (i, j) can be calculated for each pixel of the normal image.

In S303, the generation unit 204 generates an output image using the object data and rendering parameters acquired in S301 and the shape feature amount calculated in S302. In the present embodiment, the specular reflection component of the reflected light is regarded as a characteristic reflection component in the texture of the object, and an output image in which the specular reflection component is emphasized as the shape of the object is closer to the plane is generated. FIG. 4 is a flowchart showing the details of the process (S303) for generating an output image.

In S401, the feature image generation unit 205 gives the normal vector N (i, j) before smoothing to the equations (4) and (5) to each pixel (i, j) of the normal image. The corresponding specular reflection component _ISr (i, j) is calculated. Further, using the shape feature amount F (i, j) calculated in S302, the specular reflection component corresponding to each pixel (i, j) of the normal image is emphasized according to the equations (9) to (11).
_{I'Sr (i, j) = I Sr (} i, j) × F _Emphasize (i, j) ... Equation (9)
F _Emphasize (i, j) = α × F _Flat (i, j) +1 ... Equation (10)
F _Flat (i, j) = 1 / (1 + F (i, j)) ... Equation (11)

Here, the F _Emphasize (i, j) in the equation (10) is the degree of emphasis on the pixel (i, j), and the F _Flat (i, j) in the equation (11) is the plane in the pixel (i, j). The degree. Further, α (> 0) is a parameter that defines the upper limit of the degree of emphasis, and may be acquired by a user instruction via the input I / F 106, or a predetermined constant may be used. The specular reflection component _{I'Sr (i, j) obtained by the formula (9) is larger than the original specular reflection component I Sr (} i, j) as the shape feature amount is smaller (the surface shape is closer to a plane). Become. Further, in the equation (9), since the specular reflection component calculated by using the normal vector N before smoothing is multiplied by the degree of enhancement, each change in the reflection intensity based on the spatial distribution in the normal direction is emphasized. FIGS. 6A and 6B show examples of the specular reflection component before emphasis and the specular reflection component after enhancement, respectively. The specular reflection component of the rectangular parallelepiped 501 is emphasized more strongly than the sphere 502. The obtained specular reflection component _I'Sr (i, j) after enhancement is recorded in each pixel as a pixel value of the feature image and sent to the synthesis unit 207. In the present embodiment, by calculating the shape feature amount for each region in S302, the edge portion of the plane portion of an object having a small number of sharp edges and most of which is a plane (for example, a stepped object). The degree of emphasis can be increased regardless of the change in the normal direction of. It should be noted that the shape feature amount F (i, j) or the flatness or the emphasis is smoothed between the neighboring regions so that the image does not become unnatural due to the sudden change in the emphasis between the regions divided by S302. The specular reflection component may be emphasized. As for the smoothing process, a known filter process is used in the same manner as described above.

In S402, the base image generation unit 206 calculates I _Dr by the equation (2) and I _Ar by the equation (3). For N in equation (2), the normal vector N (i, j) before smoothing is used. Further, the reflection component I _DA (i, j) other than the specular reflection component corresponding to each pixel (i, j) of the feature image generated in S401 is calculated according to the equation (12). The reflection component other than the specular reflection component is the sum of the intensity of the diffuse reflection component and the intensity of the ambient light component.
I _DA (i, j) = I _Dr (i, j) + I _Ar (i, j) ... Equation (12)

FIG. 7 shows an example of a reflection component other than the specular reflection component. The obtained reflection component I _DAr (i, j) other than the mirror surface reflection component is recorded in each pixel as a pixel value of the base image and sent to the compositing unit 207.

In S403, the synthesizing unit 207 synthesizes the feature image generated in S401 and the base image generated in S402 according to the equation (13), and uses this as an output image.
I'(i, j) = _I'Sr (i, j) + I _DAr (i, j) ... Equation (13)

FIG. 8A shows an example of an image rendered without the enhancement process in S401. Further, FIG. 8B shows an example of an output image in the present embodiment. In the output image of FIG. 8 (b), the gloss of the rectangular parallelepiped 501 composed of flat surfaces is emphasized as compared with the rendered image of FIG. 8 (a), and the texture of the object is emphasized and expressed. It becomes. The output image data representing the output image obtained by the output image generation process is output to the output device 110 via the output I / F 107. Alternatively, it is recorded in a storage device such as HDD 104.

According to the present embodiment described above, the gloss of the object can be emphasized in consideration of the shape of the surface of the object, whereby it is possible to easily generate an image in which the texture of the object is easily perceived. Become.

<Modification example>
In S302, the shape feature amount is calculated for each region where the normal image is divided, but one shape feature amount may be obtained from the entire normal image (without dividing the region). Further, the variation (variance) may be obtained directly from the normal vector on the surface of the object and used as the shape feature amount without generating the normal image. In addition to the variation of the normal vector, the curvature of the object surface may be used as the shape feature quantity.

Further, in the generation of the feature image of S401, an example of emphasizing the specular reflection component using the equation (9) has been described. However, a gamma curve or an S-shaped curve is set according to the shape feature amount, and a tone curve based on the gamma curve or the S-shaped curve is set. The specular reflection component may be emphasized by using the correction.

[Embodiment 2]
The normal direction of the object surface is determined by the orientation of the surface. Further, the intensity of diffusely reflected light and specularly reflected light is generally modeled by a function in the normal direction such as Eq. (2) and Eq. (4). Therefore, the characteristics of the surface shape of the object also appear in the reflected light. For example, when the shape of an object is a plane, its normal direction is constant regardless of the location, and the variation in the intensity of reflected light becomes smaller than in the case of a complicated shape in which a surface faces various directions. Therefore, in the present embodiment, the degree of variation in the intensity of the reflected light is used as the shape feature amount. The method of calculating the shape feature amount in S302 described above is different between the first embodiment and the present embodiment. Hereinafter, the points different from those of the first embodiment will be briefly described.

First, based on the object data acquired in S301 and the rendering parameters, normal rendering is performed to generate a reference image. That is, the intensity I of the reflected light of the mesh constituting the object included in the angle of view of the rendering is calculated according to the equation (1) and recorded as the pixel value of the reference image.

Next, in S302, the degree of variation in the intensity of the reflected light is calculated using the pixel values I (i, j) of the reference image, and this is used as the shape feature amount. In this embodiment, the standard deviation σ of I (i, j) shown in the equation (14) is used as the degree of variation.

Here, Img represents the entire reference image, and num (Img) is the number of pixels of the reference image.

Finally, in S303, the degree of gloss enhancement is calculated based on the shape feature amount σ, and an output image in which the gloss is emphasized is generated according to this degree. Specifically, the shape feature amount F (i, j) in the first embodiment may be replaced with the shape feature amount σ in the present embodiment, and the same processing as in the first embodiment may be applied. At this time, the degree of enhancement obtained by the equation (10) becomes a large value when the fluctuation of the pixel value of the reference image representing the reflected light is small.

According to the second embodiment described above, the shape of the object can be considered based on the intensity of the reflected light of the object, and the gloss of the object can be emphasized. This makes it possible to easily generate an image in which the texture of the object is easily perceived.

When a plurality of objects are included in the angle of view of rendering, the corresponding image area may be extracted for each object and the shape feature amount may be calculated for each area. In that case, the gloss can be emphasized to a different degree for each object.

[Other embodiments]
The present invention supplies a program that realizes one or more functions of the above-described embodiment to a system or device via a network or storage medium, and one or more processors in the computer of the system or device reads and executes the program. It can also be realized by the processing to be performed. It can also be realized by a circuit (for example, ASIC) that realizes one or more functions.

100 Image processing device 201 1st acquisition unit 202 2nd acquisition unit 203 Calculation unit 204 Generation unit

Claims (11)

A first acquisition means for acquiring shape information representing the shape of an object surface and reflection characteristic information representing the reflection characteristics of the object, and
A second acquisition means for acquiring viewpoint information regarding a viewpoint for viewing the object and light source information regarding a light source that illuminates the object.
Based on the reflection characteristic information, the viewpoint information, the light source information, and the shape information, the reflection of light of the object so as to increase the degree of emphasis as the degree of flatness of the shape increases in the image data representing the object. A means of emphasizing strength and
It has an output means for outputting the image data representing the object whose reflection intensity of light is emphasized by the enhancement means.
An image processing apparatus characterized in that the degree of flatness of the shape is a degree of flatness of a global shape different from the fine uneven shape of the surface of the object . The image processing apparatus according to claim 1, wherein the case where the flatness of the shape is high is the case where the dispersion of normals in the global shape is small. The case where the flatness of the shape is high is the case where the dispersion of the light reflection intensity in the global shape obtained based on the reflection characteristic information, the viewpoint information, the light source information, and the shape information is small. The image processing apparatus according to claim 1, wherein the image processing apparatus is provided. The image processing apparatus according to any one of claims 1 to 3, wherein the viewpoint information is a position of the viewpoint, a line-of-sight direction from the viewpoint, and a range seen from the viewpoint. The light source information according to any one of claims 1 to 4, wherein the light source information is the position of the light source, the direction in which the light from the light source is directed, and the intensity of the light emitted by the light source. Image processing device. The enhancing means is characterized in that it emphasizes the light reflection intensity of the object based on the enhancement degree for enhancing the light reflection intensity which is proportional to the flatness degree of the shape. The image processing apparatus according to any one of 1 to 5. The image processing apparatus according to any one of claims 1 to 6, wherein the enhancing means enhances the reflection intensity of light for each region of the object. Further having a smoothing means for smoothing the degree of emphasis between regions in the vicinity of the object.
The image processing apparatus according to claim 7, wherein the enhancing means enhances the reflection intensity of light for each region of the object based on the enhancement degree smoothed by the smoothing means. 1. Item 8. The image processing apparatus according to any one of items 8. A program for making a computer function as each means of the image processing apparatus according to any one of claims 1 to 9. The first acquisition step of acquiring the shape information representing the shape of the object surface and the reflection characteristic information representing the reflection characteristic of the object, and
A second acquisition step of acquiring viewpoint information regarding a viewpoint for viewing the object and light source information regarding a light source that illuminates the object.
Based on the reflection characteristic information, the viewpoint information, the light source information, and the shape information, the reflection of light of the object so as to increase the degree of emphasis as the degree of flatness of the shape increases in the image data representing the object. An emphasis step that emphasizes strength, and
It has an output step for outputting the image data representing the object whose reflection intensity of light is enhanced by the enhancement step.
An image processing method characterized in that the flatness of the shape is a flatness of a global shape different from the fine uneven shape of the object surface .

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