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Monocular Multiple Image Recovery

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3-D Computer Vision

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Abstract

Obtaining multiple images with redundant information can also be accomplished by collecting changing images of scene at the same location. These images can be obtained with only one (fixed) camera, so it is also called the monocular method. This chapter will analyze the imaging process from the light source to the scene and then to the lens, showing that the image gray level depends on the intensity of the light source and the reflection characteristics of the scenery, as well as the geometric relationship between them. This chapter will discuss the establishment of the relationship between the image gray level and the orientation of the scenery, and the orientation of the scenery is determined by the change of the image gray level. This chapter will introduce how to detect the motion of the scenery and uses the optical flow equation to describe and solve the principle and several special cases of the optical flow equation. This chapter will further introduce the realization of the restoration of the shape and structure of the scenery by the solution of the optical flow equation. Here, the analytical optical flow equation is solved by the transformation of the coordinate system.

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References

  1. Jähne B, Hauβecker H, Geiβler P. Handbook of Computer Vision and Applications: Volume 1: Sensors and Imaging. Academic Press. 1999.

    Google Scholar 

  2. Chen Z H, Zhang Y-J. A binocular Helmholtz stereo method for measuring objects with highlights. Journal of Image and Graphics, 2010, 15(3): 429-434.

    Google Scholar 

  3. Horn B K P. Robot Vision. MIT Press. 1986.

    Google Scholar 

  4. Zhang Y-J. Image Engineering, Vol.2: Image Analysis. De Gruyter, 2017.

    Google Scholar 

  5. Ballard D H, Brown C M. Computer Vision. Prentice-Hall. 1982.

    Google Scholar 

  6. Forsyth D, Ponce J. Computer Vision: A Modern Approach, 2nd Ed. Prentice Hall. 2012.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Electronic Engineering, Tsinghua University, Beijing, China

    Yu-Jin Zhang

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  1. Yu-Jin Zhang
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Self-Test Questions

Self-Test Questions

The following questions include both single-choice questions and multiple-choice questions, so each option must be judged.

  1. 7.1

    Photometric Stereo

    1. 7.1.1

      Imaging involves light source, scenery, and lens, (·).

      1. (a)

        The light emitted by the light source is measured by intensity, and the light received by the scenery is measured by illuminance.

      2. (b)

        The light emitted by the scenery is measured by intensity, and the light received by the lens is measured by illuminance.

      3. (c)

        The light from the light source incidents to the scenery at a certain angle.

      4. (d)

        The light from the scenery incidents to the lens at a certain angle.

    [Hint] Refer to the flowchart from the light source through the scenery to the lens in Fig. 7.1.

    1. 7.1.2

      The brightness of the image obtained after imaging a 3-D scenery is proportional to (·).

      1. (a)

        The shape of the scenery itself and its posture in space

      2. (b)

        The intensity of light reflected when the surface of the scenery is illuminated by light

      3. (c)

        The light reflection coefficient of the surface of the scenery

      4. (d)

        The product of the light reflection coefficient on the surface of the scenery and the intensity of the light reflected on the surface of the scenery when illuminated by light

    [Hint] The light reflection coefficient is related to the reflected light intensity.

    1. 7.1.3

      For Lambertian surfaces, the incident and observation mode correspond to (·).

      1. (a)

        Fig. 7.6a

      2. (b)

        Fig. 7.6b

      3. (c)

        Fig. 7.6c

      4. (d)

        Fig. 7.6d

    [Hint] The Lambertian surface is also called the diffuse reflection surface.

    1. 7.1.4

      For an ideal specular reflection surface, the incident and observation mode correspond to (·).

      1. (a)

        Fig. 7.6a

      2. (b)

        Fig. 7.6b

      3. (c)

        Fig. 7.6c

      4. (d)

        Fig. 7.6d

    [Hint] The ideal specular reflection surface can reflect all the incident light from the (θi, ϕi) direction to the (θe, ϕe) direction.

  2. 7.2

    Shape from Illumination

    1. 7.2.1

      To represent the orientation of each point on the surface of the scenery, (·).

      1. (a)

        One can use the orientation of the tangent surface corresponding to each point on the surface.

      2. (b)

        One can use the normal vector of the tangent plane corresponding to each point on the surface.

      3. (c)

        One can use two position variables corresponding to the intersection of the normal vector and the surface of the sphere.

      4. (d)

        One can use the unit observation vector from the scenery to the lens.

    [Hint] What is needed is to represent the characteristics of the scenery itself.

    1. 7.2.2

      In the reflection image obtained by illuminating the Lambertian surface with a point light source, (·).

      1. (a)

        Each point corresponds to a specific surface orientation.

      2. (b)

        Each circle corresponds to a specific surface orientation.

      3. (c)

        It contains information on surface reflection characteristics and light source distribution.

      4. (d)

        It contains the relationship between the brightness of the scenery and the surface orientation.

    [Hint] The R in the reflection image R(p, q) corresponds to the surface brightness of the scenery, and (p, q) corresponds to the surface gradient of the scenery.

    1. 7.2.3

      There is an ellipsoidal object x2/4 + y2/4 + z2/2 = 1 with an ideal specular reflection surface. If the incident light intensity is 9 and the reflection coefficient is 0.5, the intensity of the reflected light observed at (1, 1, 1) will be approximately (·).

      1. (a)

        3.8

      2. (b)

        4.0

      3. (c)

        4.2

      4. (d)

        4.4

    [Hint] Calculate the intensity of reflected light specifically, and pay attention that the incident angle and the reflection angle of the specular reflection surface are equal.

  3. 7.3

    Optical Flow Equation

    1. 7.3.1

      The optical flow expresses the change of the image. The following cases where there is optical flow (optical flow is not 0) include (·).

      1. (a)

        The moving light source illuminates the object that is relatively stationary with the camera

      2. (b)

        The fixed light source illuminates the rotating object in front of the fixed camera

      3. (c)

        The fixed light source illuminates moving objects with different reflective surfaces

      4. (d)

        The moving light source illuminates a moving object with an invisible brightness pattern on the surface

    [Hint] Consider the three key elements of optical flow.

    1. 7.3.2

      Only one optical flow equation cannot uniquely determine the optical flow velocity in two directions, but (·).

      1. (a)

        If the object is regarded as a rigid body without deformation, then this condition can be used to help solve the optical flow equation.

      2. (b)

        If the ratio of the optical flow components in the two directions are known, the optical flow in the two directions can also be calculated.

      3. (c)

        If the acceleration of the object movement in the image is set to be very small, then this condition can be used to help solve the optical flow equation.

      4. (d)

        If the gray level changes uniformly but there are only a few sudden changes in the image, it can also be used to calculate the optical flow in two directions.

    [Hint] The establishment of the optical flow equation does not mean that it is solvable.

    1. 7.3.3

      In solving the optical flow equation, from the perspective of rigid body motion, the constraint that the spatial rate of change of the optical flow is zero is introduced; from the perspective of smooth motion, the constraint that the motion field changes slowly and steadily is introduced, (·).

      1. (a)

        Compared with the two constraints, the former is weaker than the latter

      2. (b)

        Compared with the two constraints, the former is as weak as the latter

      3. (c)

        Compared with the two constraints, the former is stronger than the latter

      4. (d)

        Compared with the two constraints, the former is as strong as the latter

    [Hint] Compare the representations of two constraints.

  4. 7.4

    Shape from Motion

    1. 7.4.1

      If the longitude of a point in space is 30°, the latitude is 120°, and the distance from the origin is 2, then its Cartesian coordinates are: (·).

      1. (a)

        x = \( \sqrt{6} \)/2, y = \( \sqrt{3} \), z = −1

      2. (b)

        x = \( \sqrt{6} \)/2, y = \( \sqrt{3} \)/2, z = −1

      3. (c)

        x = \( \sqrt{6} \)/2, y = \( \sqrt{3} \)/4, z = −2

      4. (d)

        x = \( \sqrt{6} \)/2, y = \( \sqrt{3} \), z = −2

    [Hint] Judge according to the coordinate conversion equation.

    1. 7.4.2

      If the Cartesian coordinates of a point in space are x = 6, y = 3, z = 2, then its spherical coordinates are (·).

      1. (a)

        ϕ = 30°, θ = 67°, r = 10

      2. (b)

        ϕ = 40°, θ = 73°, r = 9

      3. (c)

        ϕ = 50°, θ = 67°, r = 8

      4. (d)

        ϕ = 60°, θ = 73°, r = 7

    [Hint] Judge according to the coordinate conversion formula.

    1. 7.4.3

      Consider Fig. 7.25, which is/are used to illustrate the finding of the surface direction? (·).

      1. (a)

        In Fig. 7.25b, the ZOR plane coincides with the YZ plane.

      2. (b)

        In Fig. 7.25b, the ZOR plane does not coincide with the YZ plane.

      3. (c)

        In Fig. 7.25c, the ZOR’ plane coincides with the XY plane.

      4. (d)

        In Fig. 7.25c, the ZOR’ plane does not coincide with the XY plane.

    [Hint] Analyze according to Fig. 7.25a.

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Zhang, YJ. (2023). Monocular Multiple Image Recovery. In: 3-D Computer Vision. Springer, Singapore. https://doi.org/10.1007/978-981-19-7580-6_7

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  • DOI: https://doi.org/10.1007/978-981-19-7580-6_7

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-19-7579-0

  • Online ISBN: 978-981-19-7580-6

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