Using Space Effectively: 3D

From CS294-10 Visualization Sp11

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Lecture on Mar 28, 2011




  • Chapter 2, Projection Systems. In Art and Representation. Willats (pdf)
  • Chapter 8: Marginal Distortions. In The Psychology of Perspective and Renaissance Art. Kubovy (pdf)
  • What object attributes determine canonical views? Blanz et al. (html) (pdf) (alt pdf)

Optional Readings

  • Artistic Multiprojection Rendering. Agrawala et al. (html)
  • Automatic View Selection Using Viewpoint Entropy and its Application to Image-Based Modelling. Vázquez et al. (pdf)
  • Artistic Composition for Image Creation. Gooch et al. (pdf)
  • Gallery of Map Projections

Michael Hsueh - Mar 29, 2011 03:20:02 am

The lecture and readings covered quite a few types of projections. I was surprised in that there was less emphasis given to realistic perspective projections than I expected. I expected it to be the projection that is most intuitive to humans, given that it is most similar to how see the world. In reality, it is often easier to deal with projections that simplify the display of important aspects of objects being viewed. These projections may be less "visually realistic" but more empirically accessible. I think the reasons for this connects to some of the findings of the Blanz et al. paper on canonical views.

The experiments run by Blanz discovered that there exists some sort of hierarchy in what factors are considered when a person decides how to view an object. In most cases (except for imagined views), the viewer minimizes the number of object self-occlusions so as to maximize the number of details presented. In addition to this constraint, a familiar/recognized item is also subject to natural upright orientation (taking into account gravity, etc.). All of these behaviors aim to communicate important parts of the object in a clear, efficient manner. However, when the view is *imagined*, obscuring views are frequently chosen. One explanation is that people have more difficulty envisioning detailed views of objects, and thus simple and obscuring views are chosen. This tendency also influences our preference for simpler, parallel projections over more perceptually accurate projections (as mentioned above). I definitely felt that the example 3-point perspective images required more mental exhaustion in order to extract useful mental models of the scenes.

The Blanz paper explicitly omits aesthetics as a factor in its investigation of canonical views. I definitely wonder if aesthetics plays an important role. The experiments showed an interesting and strong asymmetry in view orientation when the participants were asked to envision objects. The paper notes this peculiarity but does not venture guesses about why it exists. It reminded me of another, similar phenomenon observed in the study of aesthetics. The phenomenon is explained with an example: Consider two similar pictures... The first picture is of a house in the distance near the horizon. The house is drawn on the right half of the picture. A path begins in the foreground, at the bottom left portion of the page, and ventures off, leading to the house in the distance. The second picture is exactly the same except mirrored horizontally. That is, the path starts in the bottom right foreground and ventures off to a house in the horizon. The house is in the left half of the picture. Nearly all people have an aesthetic preference for the first picture, but the reason is unclear. I would not be surprised if the underlying aesthetic phenomena is related to the asymmetric trend seen in Blanz's experiments.

Brandon Liu - Mar 29, 2011 02:00:18 pm

In the Blanz paper, I would have liked to see more examples of asymmetrical objects in the experiments, for example, a well-known asymmetrical building or scene. All of the example objects had at least one plane of symmetry except for the dog, shoe, and cactus. It seems that the choice of perspective would be to reduce redundant information. Also, it was unclear as to whether there was consistency across choices: "Participants did not consistently select the same side for all of the objects"... does this mean that there wasn't consistency across all participants, or there was no consistency within one participant? I would be curious to see if within one participant, consistent views were chosen across items. Finally, it would be interesting to see not just the final choice of viewing perspective in experiment 1, but also the three-dimensional path the participant took to explore all the different perspectives. This may reveal more information about how that specific view was chosen.

Dan - Mar 29, 2011 04:26:49 pm

I thought it was a great application of the different projects discussed to fix photos taken from wide-angle lenses. Additionally, combining different types of projections was a great idea and I liked the UI for the software demoed in class. The ability to make constraints of straight lines and optimizing the projections to make the best image worked very well.

The Willats paper starts out by formally describing a projection of geometry onto a two-dimensional plane, and the notions of perspective, oblique, and orthogonal projections in respect to the camera obscura, or what we now call a camera. Engineering drawings typically used three subclasses of orthogonal projections, which were denoted as the isometric, diametric and trimetric projections. The main point was that these projection systems have no hold in "psychological reality"! But what does the author mean by this? The author wants us to question how close the representation is to the actual geometry being projected. Mostly because there are assumptions about these drawings that don't make sense, for example, the fact the the viewer is at an infinite distance for orthogonal projections.

Krishna - Mar 29, 2011 04:47:07 pm

While Blanz reports on what viewpoints are preferred by people, Vazquez et al report a technique that can automatically find most informative viewpoints of an object.Their motivation comes from the problem of generating a set of images of an object for image based rendering. Typically, image based rendering would require huge number of images, by developing a technique that can automatically find best views of an object, they wanted to reduce the number of images that would be needed for image based rendering.

Their approach quantifies the information present in a viewpoint by using the notion of a viewpoint entropy. To compute the entropy, they consider a random variable that can take Nf discrete values where Nf is the number of faces in the viewpoint. They compute the probability of the random variable taking a value, corresponding to a face, to be the ratio of the area occupied by the face to the total area of the sphere, taken from a viewpoint, that inscribes the scene. In this sense, the probability value represents how visible a face is given a viewpoint. Viewpoints with increasing entropy of the so defined random variable are better because a higher entropy would mean faces being more visible.

I believe this technique will be useful when designing automatic layout for visualizations that use 3D. Most of the layout algorithms we have discussed so far use position and size as the major parameters to optimize, visualizations that use 3D should probably optimize on the visibility of the faces of the objects they use.

Siamak Faridani 18:29, 29 March 2011

Related to the lecture, one thing I have been wondering is that why people prefer non-perspective projections? I imagine the answer would be related to how we learn and interpret objects. For example children see a drawing of an elephant in their books and they can then easily recognize a real elephant in a movie. This to me is a fascinating phenomenon, children like the drawing better and I have seen more books with drawings than with real photos. This is fascinating that an abstraction of an object is more preferred than the actual object. Similarly in this setting orthogonal projections seem to be preferred when compared to perspective projections. Especially three point projection.

With regards to John Willat's book chapter I have two questions: first I am wondering if there is a taxonomy (an a cheat sheet) for projection classification. What I mean is that let's say I am designing a 3D visualization system, is there any article or software tool that can get a number of inputs (for example whether or not I want to keep the length of lines or whether or not I'd like to maintain the angles between lines) and come up with an optimal projection? are there user studies that actually show that CAD users always prefer Isometric views? I come from aerospace and mechanical engineering background and I have used a number of different CAD software, I used to use isometric views a lot simply because that is always the default view in CAD software packages. Althoguh I am wondering if Autodesk has really tested whether or not it is the best projection for engineers.

Michael Kubovy's article was extremely interesting. The analysis of "School of Athens" was extremely interesting. Although I am not sure if painters change their projection intentionally. Regarding thI am wondering if we can come up with a number of conditions when we need to change the projection (for example we can develop a content aware tool that when it sees a sphere switches the projection and make it a circle). Or perhaps we can develop a tool that can convert a painting from Raphael's style to Leonardo's :) Although it seems that Agrawala et al's work on "Artistic Multiprojection Rendering" is very similar to this idea.

Sally Ahn - Mar 29, 2011 09:07:30 pm

This lecture made me think about the appropriate level and portrayal of realism in 2D images. It was interesting to see that images with distorted perspective projections could appear less distorted than simple linear perspective projections. Moreover, I was surprised to learn that many artists had realized this and deliberately altered the perspective projections of their paintings my combining different projection methods to create a more "realistic" image (as in the "School of Athens" we saw in lecture). This reminded me how important it is to consider psychophysics rather than physics alone when trying to render our three dimensional world as a 2D image.

The Blanz paper conducts an in-depth study on such psychological factors for canonical views, and their results suggest that off-axis views are better suited for recognition while axis-aligned views are better representations of "imagined" views. As the authors point out, this makes sense when you consider the tasks involved for recognition and retention: the former requires interpreting a given image, so one would desire a view that provides the most information (number of surfaces visible) whereas the latter requires retaining a mapping of a concept to an image, so one would want to minimize the amount of data required for that mapping. As for the difference between right-handed and left-handed participants, I wonder if functional considerations seemed to be absent from left-handed people because they were more familiar with images of the test objects created by the demographically dominant right-handed people. I imagine that the lighting direction may have also affected these preferences, and it would be interesting to see these results under different lighting conditions.

Michael Cohen - Mar 29, 2011 11:01:46 pm

I thought the oblique projections were particularly intriguing. It's a projection that is patently unlike any pattern of light that would actually strike our eye from a 3D object (because our retinas respond to light head-on, not at an angle) and yet it looks reasonably natural, for instance in the folk art farm painting in Willats. I wonder if its naturalness in that context has to do with the fact that houses in the country are often seen at a distance, while moving, so that although we obviously can't see both sides head-on simultaneously, we do develop a mental image of the scene that includes all sides as we travel by (and we do it rather quickly these days, if we're traveling by car). It also seems, though, that the technique is only likely to appear natural when applied to something fairly box-like, because it can be unfolded without seams. Trying to see both the front and side of a person or animal would likely seem more intentionally cubist; the interplay of projection and content seems quite important in forming our perceptions.

Saung Li - Mar 29, 2011 10:57:41 pm

I found the article on marginal distortions to be quite interesting. We can look at cubes from any perspective and still be able to recognize them. However, if we look at a sphere not on the principal ray it will look something like an ellipse. What could be the reason for why our visual system is tolerant of variations in cubes but not spheres? I would expect a sphere to look like a sphere when looking at it from any angle, so the distortion is quite surprising to me. The article mentions "...artists have always accepted the primacy of perception over geometry...", yet I see all these geometric measurements such as angle lines in the images. These measurements can help but don't apply to every visualization, as there are images where people don't have to measure out the angles and such to make a compelling image. One thing I'm interested in knowing is if there are more rules to deal with marginal distortions of images seen from the computer. I would expect there to be more "standards" as people probably look at the screen from the same angle.

David Wong - Mar 30, 2011 01:53:31 am

I really enjoyed this lecture and topic on projections from 3-D to 2-D. I haven't had previous exposure to the field so it was particularly eye-opening. On one hand, I now have a better appreciation of art and how artists like Cezanne, Uccelo, and Raphael have all used multiprojection in their paintings to convey different meanings, with Cezanne using it to create tension, Uccelo using it to enhance the view, and Raphael using it to improve recognition of the people in the foreground. Also, I thought the idea of using different projections in an optimization algorithm to transform a fish-eye version of an image into an image with less distortion that would occur with wide-angle lenses was really interesting. Perhaps there can be future work in automating the process. If there are multiple fish eye pictures or pictures taken with different lenses, a machine learning algorithm can identify which lines should be marked as being straight and run an optimization on those lines.

Manas Mittal - Mar 30, 2011 03:17:18 am

I thought Siamak's comment was very interesting and insightful. Why do children prefer a hand-drawn images as opposed to pictures. I think the answer might be that hand-drawn pictures easily accentuate whats important and whats not (similar to what the Linedrive maps do). - Mar 30, 2011 12:28:44 pm

For me, the key take away point from the lecture and the reading was the discussion of perspective in terms of an object's secondary geometry. In other words, as someone interested in visualization, I care most about the distortions created by each kind of projection, and what faces, lines, and lengths are preserved by the projection. Since each projection is a different mapping of data to visual variables, there is a trade-off among them. And the reading made this point clear. Willats explained the use of axonometric projection for architectural drawings because it gives the viewer a look inside the building. Similarly, isometric projections work well for engineering drawings because they provide general views of an object, but maintain the property that the true lengths of rectangular edges are preserved (with much less perceived distortion than axonometric projection). It would have been nice if the lecture went into more detail on the trade-offs of the different perspective systems in the context of info vis, where appropriate.

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