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Photometric Stereo Reconstruction. Dr. Maria E. Angelopoulou. (1). Photometric Stereo (PS) Basics. Input images: same viewpoint / different illumination directions Varying albedo values → minimum of 3 illumination directions

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photometric stereo reconstruction

Photometric Stereo Reconstruction

Dr. Maria E. Angelopoulou

photometric stereo ps basics

(1)

Photometric Stereo (PS) Basics
  • Input images: same viewpoint / different illumination directions
  • Varying albedo values →minimum of 3 illumination directions
  • The measured pixel intensities and actual albedo for a given patch o are related as follows
  • Outputs: orientation & albedo of each surface facet
  • Height map produced after integration of the surface normals.

2

pros cons of ps compared to conventional stereo
Pros & Cons of PS Compared to Conventional Stereo

Pros

+ ability to operate on featureless objects

+ absence of feature matching errors

+ computational simplicity

Cons

controlled imaging conditions

inaccurate simplifying assumptions

need for off-line calibration sessions & exclusive access to the imaging system

3

objective
Objective

Provide an autonomous, purely data-driven PS reconstruction system that is suitable for real-life applications.

Focus on: uncalibrated flatfielding & uncalibrated light estimation.

Diffuse light component as a degradation factor for intended directional lighting. Indicate up to which ratio of ambient to directional light component photometric stereo gives useful reconstruction outputs.

4

the inverse square law of light propagation
The Inverse-Square Law of Light Propagation
  • Fundamental assumption of PS:

The variation in brightness for a given pixel is solely dependent on the angle between the illumination vector and the surface normal at the corresponding real-world surface facet.

  • In practice the inverse-square law of light propagation renders the above assumption inaccurate.
  • To correct the input data appropriately, flatfielding may be employed. Flatfielding employs a set of reference images captured at a dedicated imaging session under the same imaging conditions as the main session. The illumination variations of the reference images is solely due to inhomogeneities of the system.
standard calibrated flatfielding technique
Standard Calibrated Flatfielding Technique

Use a grey piece of card as calibrating device.

Photograph the card multiple times under the same illumination as the main imaging session.

Perform 2D 2nd order polynomial fitting on the flatfielding reference images to smooth out high frequency noise. This gives the illumination fields .

For every point of the image plane, the new pixel value is computed as

(2)

6

uncalibrated flatfielding
Uncalibrated Flatfielding
  • Intensity values decrease across the kth illumination field from the brightest point to the darkest point. Due to the inverse-square law, the 2D illumination field can be approximated with
  • Only radial distance matters, and thus
  • Placing the origin of the Cartesian coordinate system at the brightest point:

(3)

(4)

(5)

8

uncalibrated flatfielding1

(7)

Uncalibrated Flatfielding
  • Employing constraints (4) and (5), we get:

(6)

  • In (6) the origin of the coordinate system moves to the brightest point of each kth image. Instead of moving the origin for each k, it is more convenient to express (6) on the fixed image coordinate system as:
uncalibrated flatfielding2
Uncalibrated Flatfielding

(11)

  • Find the values of the brightest and darkest points:

(8)

(10)

(9)

  • Consider the location of the brightest and darkest points:
ps reconstruction
PS Reconstruction
  • no flatfielding, (b) calibrated flatfielding,

(c) uncalibrated flatfielding

standard calibrated estimation of illumination directions
Standard Calibrated Estimation of Illumination Directions

- The relationship between surface gradients and brightness is captured by the reflectance map of the surface.

- A Lambertian sphere illuminated by a point source in direction

has a reflectance map of the form:

(12)

- Let

denote the global maximum of the kth

reflectance map. It is

(13)

16

standard calibrated estimation of illumination directions1
Standard Calibrated Estimation of Illumination Directions

- Thus the surface orientation that maximizes the Lambertian

reflection component is the one for which the normal vector

points to the illumination source!

- Let the gradient at surface patch o be .

- If patch o is projected at pixel ,

then the measured image intensity at that pixel is given by the

image irradiance equation as

. (14)

17

standard calibrated estimation of illumination directions2
Standard Calibrated Estimation of Illumination Directions

- Due to equations

(14)

(13) and

the global maximum of the Lambertian reflectance map

corresponds to the maximum intensity measurement , the

luminous dot. If the latter resides at and

is the projection of the real-world patch m then

(15)

- If a Lambertian sphere is photographed, the normal vector can

be recovered at any point and can be estimated once the

luminous dot is identified.

18

uncalibrated estimation of illumination directions
Uncalibrated Estimation of Illumination Directions
  • The proposed uncalibrated illumination vector technique targets the human face class.
  • A human face can be realistically approximated with a 3D ovoid that is reconstructed on top of the face area. A 3D ovoid is given in the xyz Cartesian system by

where

19

the effect of diffuse light on ps reconstruction
The Effect of Diffuse Light on PS Reconstruction
  • PS requires the subject to be illuminated in turn by directional light sources.
  • The ambient light component that is present constitutes a degrading factor that reduces the directionality of the intended directional component.
  • Objectives:
    • Assess the PS robustness with respect to the ratio of ambient to directional illuminance.
    • Find the illuminance ratio where reconstruction is no longer informative of the actual surface.
the effect of diffuse light on ps reconstruction experimental setup
The Effect of Diffuse Light on PS Reconstruction: Experimental Setup
  • Floodlight connected to a dimmer provides uniform ambient illumination of varying illuminance.
  • Light-/Flash-meter used to measure both ambient and directional components.
conclusions
Conclusions
  • The proposed uncalibrated flatfielding technique is general-purpose and renders similar reconstruction results as its calibrated counterpart.
  • The proposed uncalibrated light estimation technique is a practical approach that targets the human face class.
  • The above techniques enable autonomous and reliable surface reconstruction for challenging real-world applications, such as the on-line capturing of human faces.
  • In the presence of ambient light, PS reconstruction quality decreases linearly as the illuminance ratio of the diffuse to the directional light component increases. PS provides informative outputs for illuminance ratios as high as λ=9.