Environment with Uneven Geometry

The goal of evaluating DCP with an environment with uneven geometry is to explore the effects of an unevenness of the scene geometry on low resolution boundaries, i.e. in cases where the captured scene geometry information does not follow all the ridges and troughs in a scene geometry. This evaluation is important because it is

(a) Averaged absolute percentage Errors (7 movements of light source) with respect to UPoint Bounces. The X axis number of bounce and the Y axis shows the error values.

(b) Average computation time (averaged on 7 movements of light source) with respect to UPoint Bounces. The X axis number of bounce and the Y axis shows the time in miliseconds.

Figure 5.23: Accuracy vs Speed of DCP

not always possible to have high resolution laser scanenrs to acquire the accurate geometry of the scene. A crude geometry can be acquired much simply by SfM based techniques described previously in this chapter. If the error rates are similar for high and low resolution geometry, acquiring ILFs of a complex scene and applying DCP on it could be made possible with an acceptable degree of accuracy.

Figure 5.24 shows a schematic diagram of such a geometry. Here, the actual geometry of the room on the left side with two pillars and a ridge has been shown in a top-view in the right. A high resolution geometry will cover all the unevenness in the boundaries along the dark grey lines. The red dotted line boundary is the low resolution geometry boundary which does not cover all the unevenness meticulously and provides an average scene boundary.

Figure 5.24: Schematic diagram of a room with uneven boundary. The right image is the top view of the boundary geometry of the room. The red dotted line is the low resolution boundary averaging the geometry.

Similar to the Section 5.3.1, the test environment with uneven geometry has been captured using a virtual environemnt. The virtual scene is a room with similar dimensions (14_⇥14_⇥6 units) although the walls around it are not uniform. There are pillars and ridges on the walls which are in similar proportions (0.3units in thickness, 0.6units in width) to a physical room on which the virtual environment has been loosely modeled. Figure 5.25 shows two walls of the environment. The light source is the same spotlight with the30 light cone.

5.3.2.1 Capture

The ILF captures has been done exactly similar to the previous section. All the ILF captures for the ground truths have been captured exactly same. The geometry how- ever has been interpreted in two different resolutions, i.e. the accurate description of the actual uneven geometry and the average description of the geometry not taking the unevenness into account. This does not however affect the capture process in any way because the different geometry resolutions are only relevant for mapping the ILF ray-database to their corresponding geometry.

5.3.2.2 Methodology

The evaluation has again been done by comparing the ground truth G1,1 with the simulated ILF S0,0 where the light source has been changed to match the position of the ground truth. The “base case” for the simulation is identical to the previous

Figure 5.25: Virtual Environment with pillars and ridges contributing to an uneven boundary. Right side image has spotlight placed near the edge.

environment, in the center of the room (3D global position (0,0,0)) with radiance L0= 1.

The additional variation in the comparison comes with the variation in the geometry. The distribution of UPoints has been done in two ways; (i) which follows high resolution geometry boundaries, (ii) which follows a low resolution approxi- mated geometry boundary (e.g. the red dotted line in Figure 5.24). On the basis of these two separate distribution of UPoints, the DCP is used to change the position and radiance from (x0, L0) to (x1, L1) and the the simulated indirect light is collected for both of these cases. The indirect lights are similarly retrieved from the S0,0 as well as the ground truthG1,1 which are subsequently compared to obtain the error as a measure for the accuracy of the DCP technique. This method is repeated for both the cases (high and low resolution boundaries) as well as repeated over several different ground truths with varying positions and radiances similar to the testing procedure in the previous section to get a distribution of errors against the amount of the change. The errors are then compared with the two cases to find out whether there is a significant amount of difference in them. The next section describes the results.

5.3.2.3 Position Change Propagation Evaluation

The light source movement evaluation has been done with the similar eight different environments with varying light source positions atX = 0,2,2.5,3,3.5,4,4.5,5along the global X axis with the same power of the light. Figure 5.25 shows two walls of the same environment used with light source atX= 0 and the light source at X= 4.5. Similar to the previous evaluation, this experiment usesX= 0position as the base ILF for the propagation. The reflected indirect light data from both cases are

obtained from the respective ILFs and subsequently, the average reflected luminance is calculated in the same procedure as the previous. This process is repeated for 7 different positions of the light source X = 2,2.5,3,3.5,4,4.5 and 5 for each of the two cases (high and low resolution). Similar to the previous evaluation, normalised RMSE and the absolute percentage error has been calculated compared between both cases.

Figure 5.26: RMSE values for the indirect light from scene geometry. The X axis is the unit distances from the base position of the light source as it is moved towards the right side. Y axis is Normalised RMSE calculated from the entire geometry. The blue line for High-res geometry is almost invisible due to the closeness of values in both cases.

The Root Mean-Squared Error (RMSE)values in the graphs shown in Figure 5.26 has been calculated for the luminance at 8 different positions where the SLF were moved on the global X axis. The RMSE values are normalised by the range of the baseline values. As the light source has been moved gradually towards the right hand direction of the scene, the error values in overall luminance has been calculated for indirect light bouncing off the scene geometry. Unlike the previous evaluation, the graph does not include separate red, green and blue channels but only the overall luminance for low and the high resolution geometry.

The graph shown in Figure 5.26 shows the nRMSE values for high-res and low-res geometry in blue and a dotted red line respectively. Evidently the values are so close together, they are visually almost impossible to distinguish separately. This is why a separate graph at Figure 5.27 shows the improvement of the RMSE from ow resolution geometry to the high resolution geometry for UPoint distributions. The highest improved result is near the edge atx= 5 however, the improvement is only 0.65% which is negligible. It thus can be safely said that the high resolution

Figure 5.27: Improvement (in percentage) in RMSE values for the indirect light from scene geometry while using the high resolution geometry instead of lower resolution. The improvement percentage definitely increases as the lights are moved towards the boundaries but the amount is insignificant.

geometry acquisition do not have any significant improvement in DCP performance whatsoever. For some extreme cases that may affect DCP performance, the capture must be done in a way that circumvents those problems. Section 5.3.3 discusses this issue later.

The Absolute Percentage Error is the second type of error similar to the pre- vious evaluation. It has been calculated throughout the space span of the scene geometry; i.e. the ((Voriginal Vmoved)/Voriginal) ratio for the different areas of the

captured geometry. In the graph at Figure 5.28, the errors for the high-res and low-res geometry has been shown in blue and red dotted line similar to the RMSE graph.

The average absolute percentage error can be seen increasing in the graph described in Figure 5.28 as the light source is moved towards the edge of the scene geometry. Again, it is apparent that the error values for the two different geometry resolutions are extremely close together and there is absolutely no apparent trend in the improvement form the lower to the higher resolution geometry for the absolute percentage error. This further strengthens the conclusion that there is no significant improvement in accuracy for high resolution geometry data for simple scenes. Lower resolution geometry on the other hand can be acquired with significantly much more ease than acquiring precise geometry.

Figure 5.28: Absolute percentage error for movement of light source. The X axis is the unit distances from the base position as the light source is moved towards right side. The Y axis is the percentage of error calculated from the entire geometry. the light source by comparing indirect light data with 9 different levels of change. The highest percentage of absolute error was8% at 100 times of the base radiance. This is considerably accurate and thus there were no need to re-do the radiance evaluations for the high and low resolution geometry as well, particularly, given their extremely similar performances in the movement comparison.

Similar to the previous evaluation, this was conducted with a synthetic envi- ronment given the freedom and precision to control the position and radiance of the light sources.

5.3.3 Discussion

The objective of the DCP technique was to change the direct light in ILF with indirect light fidelity. The evaluations of DCP shows average absolute percentage errors of 9.14% and RMSE of 0.017 in the test cases when the light source is moving. These error percentages are below the JND which means, the indirect light difference coming from the scene geometry from an actual ILF and an edited ILF with the DCP will not be distinguishable by naked eye.

Figure 5.29 at the end of this chapter shows a few sample scenes rendered as an example of the DCP technique at work with changing light source positions and the intensities. The DCP technique propagates the dynamic changes made to the light source to the entire indirect light stored in the ILF database. The change in the indirect light with DCP can be seen in the synthetic mirrored balls reflecting the environment in these rendering samples.

This not only solves the problem for editing ILF, but subsequently opens up many new research directions as well in terms of object relighting and video relighting in post processing. Next section will conclude this chapter.