# Compression of stereo image pairs and streams

## Summary (3 min read)

### 1 Introduction

- The limit load analysis and the complete failure analysis of a structural system are important problems in performance-based design procedure.
- Localized dissipative mechanism eliminates the mesh-dependency of numerical solutions.
- Moreover, the spreading of plasticity over the entire frame and the appearance of the softening plastic hinges in the frame is consistently accounted for in the course of the nonlinear analysis.
- With respect to the existing embedded discontinuity beam finite elements, see Armero et al. [6], [7], [8], and Wackerfuss [11], the authors use more complex material models: stressresultant elastoplasticity with hardening to describe beam material behavior and stress-resultant rigid-plastic softening to describe material behavior at the discontinuity.
- It is also capable of describing local buckling of the flanges and the web, which is, in bending dominated conditions, very often the reason for the localized beam failure.

### 2 Beam element with embedded discontinuity

- The authors consider in this section a planar Euler-Bernoulli beam finite element.
- The element can represent an elastoplastic bending, including the localized softening effects, which are associated with the strong discontinuity in rotation.
- The geometrical nonlinearity is approximately taken into account by virtual axial strains of von Karman type, which allows this element to capture the global buckling modes.

### 2.2 Equilibrium equations

- The weak form of the equilibrium equations (the principle of virtual work) for an element e of a chosen finite element mesh with Nel finite elements, can be written as: δΠint,(e) − δΠext,(e) = 0. (22) (25).
- From the virtual work of external forces δΠext,(e) the authors can get the vector of element external nodal forces fext,(e), representing the external load applied to the element.
- The authors will treat this contribution locally element by element.

### 3 Computation of beam plasticity material pa-

- In the previous section, the authors have built the framework for stress-resultant plasticity for beam finite element with embedded discontinuity.
- My can be determined by considering the uniaxial yield stress of the material σy, the bending resistance modulus of cross-section W , the cross-section area A, and the level of axial force N .
- The computation with shell model takes into account geometrical and material nonlinearity that include: plasticity with hardening and strain-softening, strainsoftening regularization, and local buckling effects.
- To determine the values of the beam model hardening and softening parameters, the authors make an assumption that the plastic work at failure should be equal for both the beam and the shell model.

### 4 Computational procedure

- In this section the authors will present a procedure for solving the set of global (mesh related) and the set of local (element related) nonlinear equations generated by using the stress-resultant plasticity beam finite element with embedded discontinuity presented in section 2.
- The authors keep them fixed once determined.

### 5 Examples

- In this section the authors illustrate performance of the above derived beam element when analyzing push-over and collapse of steel frames.
- The authors also illustrate the procedure, presented in section 3, for computing the beam model plasticity material parameters by using the shell finite element model.
- The beam model computer code was generated by using symbolic manipulation code AceGen and the examples were computed by using finite element program AceFem, see Korelc [20].

### 5.1 Computation of beam plasticity material parameters

- Kh and Ks as suggested in section 3.the authors.
- In the first step the authors applied a desired level of axial force N at the mid-point MP of the rigid cross-section, see Fig.
- The results of analyses are presented in Figs. 7 to 9.
- In Figure 8, the authors show the corresponding moment-rotation curves.
- The authors assume that the axial force has no influence on softening modulus and adopt the average value Ks(N) = −3.28 · 10 5 kN/cm 2 . (89) In Table 2 they make a point-wise comparison between the shell analysis results Mrefu , E W p,ref and EW p,ref and the corresponding beam model results.

### 5.2 Push-over of a symmetric frame

- In this example the authors present a push-over analysis of a symmetric frame.
- The material and cross-section properties of all frame members are equal.
- In the left part of the Fig. 12 the authors present the total lateral load versus utop curves.
- The nondissipative period is followed by a short period with dissipation due to material hardening only, which ends with the first activation of softening plastic hinge in one of the beam finite elements.
- In the right part of Fig. 13 the authors present locations where the softening plastic hinges appeared during the analysis.

### 5.3 Push-over of an asymmetric frame

- The total lateral load versus utop curves, where utop is horizontal displacement at the top-left corner of the frame, are presented on the left part of Fig. 15.
- After that point the difference between those two analyses is bigger.
- In the right part of Fig. 15 the authors present the dissipated energy versus utop curves.
- Namely, first there is the elastic non-dissipative phase, followed by the pure hardening dissipation phase, followed by the combined hardening and softening dissipation phase and finally the pure softening dissipation phase.

### 5.4 Bending of beam under constant axial force

- In this example the authors compare results of the beam model with results obtained by using the shell finite element model from ABAQUS.
- For that reason, the geometric and material properties are the same as those in the Section 5.1.
- The difference between the applied concentrated moment at the point MP (see Fig. 6) and M∗u thus arises due to large displacements correction.
- When the yielding and local buckling of the beam are significant and the displacements in the y direction are no longer negligible, the contribution of the axial force N to the bending moment must be taken into account.
- The prediction of the beam model for plastic work in hardening regime is in the case of geometrically linear analysis with SET1 material parameters 80% of the shell model prediction, and the prediction for plastic work in softening regime is 92% of the shell model prediction.

### 5.5 Collapse of a simple frame

- In this example the authors compare results of the nonlinear beam model with the results of the shell model.
- The geometry and the finite element mesh of the shell model is presented on the right side of Fig. 18.
- The lateral load versus utop curve (left part of Fig. 19) of the beam model with SET1 material parameters has a similar shape as the shell model curve, but the prediction of the maximum resistance of the beam model is around 84% of the shell model’s resistance.

### 6 Conclusion

- The latter is captured and stored within the macro-scale beam model in the manner which is compatible with enhanced beam kinematics with embedded discontinuity.
- The most appropriate choice of the meso-scale shell model can be further guided by the error-controlled adaptive finite element method for shell structures (by using model error estimation, see e.g.
- The multiscale procedure proposed in this paper belongs to the class of weak coupling methods, where the authors carry out the sequential computations.
- One of its main features is that detection and development of the softening plastic hinges in the frame is fully automatic, and spreads gradually in accordance with stress redistribution in the course of the nonlinear analysis.

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##### Frequently Asked Questions (16)

###### Q2. What are the future works mentioned in the paper "Compression of stereo image pairs and streams" ?

Future research will address in the short term fine-tuning the architectures and algorithms and understanding their fundamental mathematical and psychophysical efficiencies, and in the long term issues such as multiple camera schemes and object based compression methods.

###### Q3. What is the basic approach to 3D-stereoscopic imagery?

APPROACHTheir basic approach to compression of 3D-stereoscopic imagery is based on the observation that disparity, the relative offset between corresponding points in an image pair, varies only slowly over most of the image field.

###### Q4. What is the effect of a stereoscopically viewed image?

When the set is as small (in bits) as 1 to 2% of the conventionally compressed image the stereoscopically viewed pair consisting of one original and one synthesized image produces convincing stereo imagery.

###### Q5. What are the main topics that the authors need to address in the context of 3D-stere?

Topics that the authors need to address in the context of compression of 3D-stereoscopic imagery include:• Optimizing implementation of the WorldLine approach.•

###### Q6. What is the way to exploit the high correlation between temporally adjacent frames?

The successful development of compression schemes for motion video that exploit the high correlation between temporally adjacent frames, e.g., MPEG, suggests that the authors might analogously exploit the high correlation between spatially or angularly adjacent still frames, i.e., left-right 3D-stereoscopic image pairs.

###### Q7. How do you compute predictors for left and right views?

Using three cameras: compute predictors for left and right views given the middle view, transmit the middle view and the predictors, synthesize 3D-stereoscopic views at the receiver.

###### Q8. What is the fundamental issue when 3D-stereoscopy is implemented on a?

The fundamental issue is that when 3D-stereoscopy is implemented on a single display each eye gets in some sense only half the display.

###### Q9. What is the effect of a synthesis of a left-right stereo image?

Their experiments demonstrate that a reasonable synthesis of one image of a left-right stereo image pair can be estimated from the other uncompressed or conventionally compressed image augmented by a small set of numbers that describe the local cross-correlations in terms of a disparity map.

###### Q10. What is the difference between the two views?

In fact, because the two views comprising a 3D-stereoscopic image pair are nearly identical, i.e., the information content of both together is only a little more than the information content of one alone, it is possible to find representations of image pairs and streams that take up little more storage space and transmission bandwidth than the space or bandwidth that is required by either alone.

###### Q11. How much bandwidth is needed to transmit 3D-stereoscopic images?

the bandwidth must apparently be doubled to transmit 3D-stereoscopic image streams at the same spatial resolution and temporal update frequency as either flat image stream.

###### Q12. What is the difference between the two components of a 3D-stereoscopic image?

One component may be either lossless or slightly lossy, as in conventional compression of flat imagery; the other component is by itself a very lossy (or "deep") method of compression.

###### Q13. What is the way to deal with occlusions?

The human visual perception system has an effective way to deal with occlusions: the authors have a detailed understanding of the image semantics, from which the authors effortlessly and unconsciously draw inferences that fill in the missing information.

###### Q14. What is the method for initial experiments?

This is the obvious candidate for initial experiments because it is easy to code and because the authors have a strong intuitive understanding of its parameters.

###### Q15. How does the price of a 3D-stereoscopic image be extracted?

The price may be extracted in either essentially the spatial domain, e.g., by assigning the odd lines to the left eye and the even lines to the right eye, or in essentially the temporal domain, e.g., by assigning alternate frames to the left and right eye.

###### Q16. How much is the net compression of disparity?

Each disparity is a vector with two components, horizontal and vertical, so the net compression has an upper bound of 1/32, about 3%.