Using Space Effectively: 3D

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Lecture on Oct 20, 2008




  • 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. (html)
  • Artistic Composition for Image Creation. Gooch et al. (pdf)
  • Map Projections in PDF

Nicholas Kong - Oct 19, 2008 11:57:13 pm

I found the Kubovy chapter very enlightening. Previously I had thought that perspective projection completely obeyed principles of perception, so it was interesting to discover that spherical and cylindrical shapes must be treated differently.

This reading, coupled with Maneesh's work on artistic multiprojection rendering, has me wondering how much work has been done in applying applying multiple projections to scientific visualization. I'm not sure what the utility of pursuing research in this direction is, but offhand I can think of exploring anatomy as a possible application.

NickDoty - Oct 20, 2008 02:06:38 pm

I enjoyed the Blanz study for its definitive analysis of canonical views. It's a rather long paper, but it's great to see fairly conclusively that, for virtually all purposes, users prefer an off-axis view as the canonical view. Differences between familiar objects and nonsense objects are interesting too -- people like to have a consistent upright view of objects they know, and tend not to have consistent canonical views of objects they're not familiar with. And certain properties always matter -- occlusion, seeing multiple faces, etc.

Kuang - Oct 20, 2008 05:47:31 pm

In the Automatic View Selection paper, I like the application of viewpoint entropy. The author posits that the area of a project face over the area of the total scene would be a good measure of the amount of information given by the view. I was not sure if the projected area meant the actual orthogonal surface area (the latter, I think, may be a better measure).

Their description of why Kullback-Leibler distance can't be used to measure viewpoint entropy differences between two views is quite brief (maybe hand-wavy). Although, the entropy-recomputation algorithm seems like a simple dynamic programming solution to get around having to compute distances. Basically they save visited faces, and only need to compute not-yet visited faces in recomputation.

They say the search space is NP complete, and will use a greedy algorithm, but no more than that. It'd be nice if they commented more on which views to select.

Ketrina Yim - Oct 20, 2008 07:33:10 pm

It was refreshing to see that non-photorealistic rendering research has gone into aspects other than shading. By lifting the restrictions of having one global camera in a scene, multiprojection rendering could open new venues in computer-generated art. However, I think we might be a long way off from being able to render a 3D version of Hogarth's [Satire on False Perspective].

On a side note, HD View is amazing. Before this, I didn't know that gigapixel images were possible. It's an impressive amount of detail packed into one image, and I could have spent hours exploring the sample pictures.

Oh, and the owl is a statue.

Ljuba - Oct 21, 2008 01:15:03 am

The gigapixel photo in today's lecture reminded my of a photo Steve Jobs showed at the WWDC Keynote in 2007. It was a 4GB image of the reading room of the Library of Congress.

This most amazing thing about the demonstration is when he quickly zoomed through this enormous photograph revealing enough detail to easily read the titles printed on the spines of the books against the back wall.

This was my first introduction to gigapixel photography and it's truly an amazing way to elegantly catalog large amounts of spatial, organizational, and temporal information - all in a single photograph.

Simon Tan - Oct 22, 2008 12:03:28 am

I found the study of children's drawings mentioned in the lecture to be really interesting. The development from drawing a house with an orthogonal projection to one with a horizontal oblique projection was exactly the process I went through as a child.

Actually, due to my innate lack of artistic ability, I believe I stuck with drawing houses with a horizontal oblique projection for many years - houses were my favorite thing to draw for a long time, and that was the way I knew I could succeed in drawing it "right" every time.

I was hoping to see where that study led; I looked for the next projection "step", but there didn't seem to be any examples. Perhaps most children who do not grow up to be artists simply stop developing their perception for drawing after discovering the horizontal oblique projection. Or perhaps each person diverges from that stage and uses different projections based on their culture or experience.

HDView seemed to display similar technology as Photosynth, at least for the dynamic loading of finer resolution images. Photosynth does not change between different projections, as far as I know.

Scott Murray - Oct 23, 2008 09:55:59 am

I would second Simon's comments above. Willats does a great job illustrating his argument and the different forms of projection and perspective. I, too, wish he had focused on the subject of human visual development as much as he does on the historical evolution of projection systems. At what age do we first acquire the abstract thought processes needed to render real-world, 3D objects on a 2D surface using perspective? For me, I think it was somewhere between age 8 and 10, when it was first pointed out to me how straight train tracks will converge on the horizon. One I understood the concept of convergence (though I wouldn't have called it that, at the time), it was easy to start drawing cubes, boxes, rooms, and other regular 3D objects. It would be interesting to find some research on human visual systems development that has already shown when these faculties usually emerge.

Witton Chou - Oct 26, 2008 02:00:12 pm

The understanding of human perspectives has come a long way and it is certainly intriguing to observe its development throughout history. While work from the Renaissance period is invaluable in visualizing 3D space on a 2D plane, its uses have evolved over the years. Understanding how different types of lenses will yield different information in a photograph has led to things like artistic multiprojection and HDView. I was astounded how seamless and how well HDView was able to clearly zoom in on details that are very far away and made me feel like I was floating in midair looking at where our camera angle was pointed towards.

Nivay Anandarajah - Oct 26, 2008 10:05:09 pm

I found the "What object attributes determine canonical views?" and "Artistic Composition for Image Creation" to be refreshing articles on merging artistic principles with design evaluation. As it stands, heuristic rules of composition and design methodology are often kept in separate spheres. Scientist must often defer to the fine arts skills of graphic designers to create a "pleasing interface." However these graphic designers are going to school to learn heuristic rules of composition and get practice determining what designs are canonical for others. Although these are often lumped into a nebulous skill set of "artistic talent", it is not difficult to methodically compose a design. The canonical article gives a good overview of doing this empirically, while the artistic composition article gives a good overview of doing this through heuristics. I feel both these methods needs to be combined to fully embody the artistic process. An interesting topic of research would be using these principles to generate entirely new designs.

Michael So - Oct 27, 2008 01:41:41 am

I don't really understand the usefulness of combining multiple views. It looks confusing and even a bit disturbing (such as the "Unfolding an elephant" slide). The perspective distortion slide with the same photo of a lady shown through three different lenses was pretty interesting. The wide angle lens makes it look like she's smiling whereas through the other two lenses, she does not seem to be smiling. I am not sure how to apply these properties and observations on perspective to creating visualizations. I guess it has to deal with manipulating visual elements from knowledge on human perspective.

Yuta Morimoto

The effect of combining multiple views is very interesting. It includes great flexibility during image acquisition and improves image reconstruction since the image does not lose actual continuous information. It generate distorted visualization with different perspective. Apparently, It looks strange and is unfamiliar visualization for me. However, as we saw in class, projection is intrinsically distorted so that our sense of 3D projection may be depending on our experience, especially multiple center of projection.

Chris - Oct 27, 2008 10:15:38 am

The topic of marginal distortions (versus increased field of view) is a contentious issue is in the field of view of video games. For a very long time, basically all monitors had a 4:3 aspect ratio. Nowadays, there are more widescreen displays than before, and game designers need to take this into account while specifying their field of view. If you play some games (e.g, the Doom 3 demo, IIRC) on a widescreen display, you'll notice a large amount of marginal distortion which. While bad enough in a standalone image, it has a somewhat nauseating effect while moving through a 3D environment. This is just my own personal experience though, and other people have other (strong) preferences. For example, the horizontal FOV lock in Bioshock was contentious enough to warrant a wikipedia entry on it.

James Hamlin - Oct 27, 2008 01:30:56 pm

I really enjoyed the chapter from John Willats' book, Art and Representation. The prose reads well and is often even funny, and there are plenty of figures to refer to (though I wish I could see them in color, and some of the dangling references to figures not included in the excerpt disappointed me). My favorite line: "The idea of orthogonal projection as a variety of perspective with the object moved to an infinite distance away is a mathematical fiction, and engineers rarely, if ever, think of the system in this way."

Jeff Bowman - Oct 27, 2008 01:38:53 pm

The most interesting part of this lecture for me was the distinction between "good" and "bad" distortion. As some of the optical illusion slides demonstrated, there's a certain amount of color and shape distortion that the eye expects, or else things look wrong. However, the Raphael fresco illustrated that the round ball was improperly drawn, but looks more appropriate than a skewed sphere.

This has necessary effects to Tufte's work regarding perceived size and shape, because even if a shape is represented accurately, it could be perceived as being a different size or shape—all the worse when the shape conveys useful information.

Maxwell Pretzlav - Oct 27, 2008 02:16:39 pm

I found the discussion of the limits of the typical angle of vision in Kubovy very interesting. The idea that following the logical mathematical projection of a scene in perspective only works to the limits of what we can actually see is fascinating. When perspective images are drawn at a wider angle than what we can normally see, they look distorted despite the fact that the projected image follows the exact same geometric rules as images which don't appear distorted but which stay within a "possible" field of view. Kubovy seems to demonstrate that renaissance painters understood this, and his quotes of Leonardo da Vinci and analysis of Raphael's School of Athens show that renaissance painters understood that to make a painting at a wider angle than we can actually perceive, certain geometric rules had to be broken to retain realistic perception.

Calvin Ardi - Oct 27, 2008 02:59:57 pm

It was interesting to get an overview of all the different styles and perspectives used in representations, drawings, and images. I've formally learned a few of these way back when in basic drawing classes, and they are heavily studied upon in drafting/CAD courses (although many of them I didn't know the formal name for them). As Simon said earlier, it was interesting to use drawings done by children as being studied based on their projections; many of them look familiar and probably not so different than what you would find in elementary schools today. I did notice the picture (slide 36) had what I presume is something written in Greek; I wonder if there are any studies done regarding the differences in primary education across different countries and drawings/visual representations that students do.

Dmason - Oct 27, 2008 03:01:32 pm

I have to admit that I wasn't really impressed by any of the 3D visualizations we saw in class today. They either grossly distorted the data (such as the columns demonstration, where all space relations went out the window) or suggested incorrect conclusions (such as the color weaving, where the perceived gestalt color could change dramatically from person-to-person).

Every time you add more to 3D-visualization, you risk these kinds of gross distortions. I am more impressed by visualizations which use our own interpretation of three-dimensional environments. One example, for instance, we can recall from those lovely stereographic toys we used as kids [1]. In this case, I prefer the dual-images which require you cross your eyes and overlap the images. This maintains 2-dimensional information from focusing on one image, with the 3-dimensional representation as optional. Also, stereograms that require you to focus at a closer distance than the image maintains focus much better than stereograms that require you to focus at a farther distance, such as Magic Eye, which I've always hated.

If you have access to a computer, you can also quickly flip the two images, as depicted at the bottom of the above link, with an animated gif. This is extremely effective in my opinion.

Seth Horrigan - Oct 27, 2008 4:54:40 pm

I was also interested to see how childrens' drawings (and my drawings as a child) were classified (mostly orthogonal projections with a few horizontal oblique projections). Even more interesting to me though was 1604 de Vries detailing how to render realistic bodies in one-point perspective. I was also fascinated by Uccello's Sir John Hawkwood, as well as Kubovy's premise that the current piece is actually the third iteration and an acceptable compromise achieved through trial and error. The clever combination of perspectives to render the image both in a manner that gives it the appears of three dimensions, while preserving the perceived realism despite rendering the image from two mutually exclusive viewpoints is both innovative and cunning. I would like to see in person exactly what the effect is.

I appreciated Kubovy's reference to Sanders's 1963 experiment quantizing the actual range of perception without saccadic eye movement: something about the actual physical limits of human perception always interests me.

HeatherDolan - Oct 28, 2008 12:11:44 am

I liked the comprehensive overview this lecture and the readings provided for projections and 3D. I find it very interesting that different perspectives can be combined to create images/visualizations that are not technically accurate, but are still acceptable (and even pleasing from an artistic perspective) to the human eye and comprehension. We may not necessarily notice what's wrong until we see what's right (right meaning a single view/perspective). However, as pointed out in the canonical views paper, people have generally have a preferred view, at least for objects. I found the paper and the experiment (as well as the previous experiments mentioned), particularly the use of the "first imagined" view, very interesting.

As an aside, the Gigapixl project is a project to document various places and subjects by creating gigapixl images, although they lack the view change we saw with HD view. There is a really nice image gallery posted here:

Matt Gedigian - Oct 28, 2008 01:31:36 am

@NickDoty, I also liked the Blanz paper. The characterization of canonical seemed very well-developed and it was tied to a variety of different experiments. I'd like to read the referenced paper by Palmer and Rosch "Canonical perspective and the representation of objects", but I wasn't able to find that online. It's interesting to see some the ideas from Rosch's work in categorization get mixed with Palmer's work on visual perception. Go Berkeley!

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