Assembled Reliefs with Seamless Overlap

In this section we demonstrate how a simple modification of our gradient domain method can assist in modeling more sophisticated relief sculptures. The simple setup of a single object is generally satisfactory for standard applications. Here, we want to increase artistic freedom by providing a solution for combined inputs.

Such a branch of digital relief generation has not been investigated until now.

In particular, our focus is on seamless transitions between different objects or viewpoints. One application is the generation of geometric collages for which a user can easily assemble the content by positioning multiple overlapping objects.

Another field is cubism. In this type of art, multiple perspectives of one and the same object are merged into a single scene.

Again, simplicity and ease of use are the most important aspects here. This is why a composition of the input can take place directly in 3D space by arranging objects in a drag-and-drop manner, or by using a regular image editing tool to mosaic the individual height fields. In practice, we use a 32-bit TIFF format for the still depth maps. Today, most programs support this format and also provide dialogs for layers and transparency. Altogether, this makes it very convenient to generate multi-object and multi-perspective input.

3.3.1 Challenge

Different shapes, or even different views on the same object, can exhibit very different depth ranges. Figure3.15illustrates the problem. In part (a) one can see that the front view is much more salient than the side-face. The collage (b) of 4 different objects (Greek statue, bunny, cup, pharaoh mask) shows that the objects themselves inherently exhibit very different extensions. These differences reflect in large jumps along the areas where two or more elements occlude each other.

(a) (b)

Figure 3.15: An assembled height fields of two different perspectives of the David head (a) and a depth map of collage with four different shapes.

(a) (b)

Figure 3.16: A relief with obvious transitions (a) and a seamless result (b).

The great benefit of our gradient domain approach is that the outlier detection finds these transitions automatically throughout the pipeline, without the need for further intervention. The remaining challenge is that setting those areas to zero re-sults in a flat transition which emphasizes the impression of having distinct scene elements. This behavior was intended in the general pipeline, but in this scenario, it would definitely undermine the desired impression. Figure3.16 (a) depicts the result of the unmodified algorithm. One can see that the step transforms to a visi-ble seam along the transition area. Our experiments revealed that using a diffusion process or blurring those pixels in the spatial domain may lead to even worse re-sults, as they introduce additional steps between modified and unmodified entries.

It is therefore necessary to treat these singularities by appropriately manipulating the corresponding gradients before the reconstruction takes place.

3.3.2 Solution

An outlier affects its direct neighbors during the Poisson reconstruction step.

Thus, we extent the outliers mask so that adjacent pixels are also considered.

Let us denote this new binary transition mask byt. It covers all non-reliable posi-tions and can easily be derived fromousing a morphological dilation of the null entries. In other words, every binary pixel is mapped to the product of its 3x3 neighborhood.

Now we need to proceed by refilling the areas of t with meaningful values by a weighted average of the surrounding area. Therefore, we apply a Gaussian smoothing with a large support, but ignore all other masked pixels. This step reads as follows:

Here, N(i)stands for pixeli and its direct neighbors. For the standard devi-ationσ_sof the Gaussian kernelG_σs a constant value of 8 has been chosen for all of the experiments in this section. Applying this additional modification to the gradient field before the reconstruction leads to the effect which is shown in Fig-ure3.16. The unsightly seam from part (a) has successfully been removed, which results in a continuous relief (b).

We want to mention that all detected outliers are refilled. This means that ar-eas of coarser steps on an object itself are also affected and no longer lead to flat encircling lines. To be able to distinguish between the treatment of overlapping ar-eas and surface edges, another threshold value would be necessary. Nevertheless, as our experiments have shown, such a distinction is hardly required in practice.

This is demonstrated by the following results which have been achieved without another such parameter.

3.3.3 Results

Figure 3.17 contains four example reliefs achieved with this slightly extended pipeline. Parts (a) and (c) correspond to the the input height fields shown in Fig-ure3.15. The results demonstrate that the described method nicely blends together the outlines of different models or perspectives and thus supports the impression of watching a continuous scene.

The input for the first three exemplars has been assembled using an image editing tool. In contrast, the second collage in Figure 3.17 (d) has been set up right in 3D space. We want to stress that the three objects (Caesar, lion vase and bunny) do not touch in 3D. The head and the bunny are simply placed in front and over the vase such that they appear to touch in this fixed perspective. No mesh editing or similar actions have been necessary.

This simple, yet powerful, extension of the initial algorithm has proven to reliably remove disturbing transition artifacts from assembled scenes. Since the detection of singular areas comes basically for free, no additional user intervention is necessary. The described approach allows even hobby-artists to design more elaborate relief artworks in which multiple objects or perspectives appear to melt into each other.

(a) (b)

(c) (d)

Figure 3.17: Multi-perspective reliefs of the David head (a) and (b), followed by two results of geometric collages assembled from a number of different shapes (c) and (d).

Conclusion