Standards For Detection of Geometric Shapes

[CalliArcale]

This thread grew out of Maxtheknife's dissatisfaction with the response to his posts about geometry in Cydonia. I think the real nub of the problem is that no scientific standard was established for determining what is geometric and what is not. So, here's someplace where we can discuss that!<br /><br />I would like us to avoid getting off into a discussion of whether or not Cydonia (or any other extraterrestrial feature) is artificial. Instead, let us discuss the problem of finding the "true" edge in a greatly eroded structure. This is a problem relevant in many fields: from archeologists attempting to reconstruct the shape of a crumbling Maya pyramid, to software engineers developing intelligent agents to detect the presence of specific animals moving through an area. It's not an easy one, either, especially in the latter problem, where the edge must be defined with mathematical exactness (though not neccesarily precision; computer programs vary widely in their ability to do this). And of course it is significant to those wishing to determine whether there is an intelligent pattern behind the features on Mars, at least those who attack the problem by measuring the distances and relationships between those features.<br /><br />So, if you are presented with an irregular object and you wish to determine what its boundaries are, what is a good way of going about it? How do you prevent or at least detect the human tendency to see things which are not there (pareidolia)? If two or more lines appear equally likely for a given edge, how do you choose between them? And most importantly, how do you do this in a way which is reliable and which others can duplicate consistently? <div class="Discussion_UserSignature"> <p> </p><p><font color="#666699"><em>"People assume that time is a strict progression of cause to effect, but actually from a non-linear, non-subjective viewpoint it's more like a big ball of wibbly wobbly . . . timey wimey . . . stuff."</em>  -- The Tenth Doctor, "Blink"</font></p> </div>

 

[bad_drawing]

I don't want to derail this thread before it even gets going, but your post reminded me of an interesting article I read this morning that seems like it could be pertinent to this discussion. Its about how as a species we seem to be hardwired for geometry.<br /><br />http://www.msnbc.msn.com/id/10925120/<br /><br /><br /><br />

 

[bonzelite]

this is gonna become a phenomenon thread. get ready...

 

[mlorrey]

It is a common fallacy of the 'ancient astronauts' crowd to believe that distinct geometric shapes do not occur in nature. This idea is patently false, as anyone, who has ever replicated natural geometric shapes with mathematical formulae or software like Matlab, knows.<br /><br />As examples, lookee at the following:<br /><br />http://www.xtec.es/ceip-pompeufabra-lloret/ciencia/english/natu0.htm<br /><br />http://www.infinitetechnologies.co.za/articles/geometry1.html<br /><br />http://www.geniaal.be/html/002mainscience.htm<br />http://www.geniaal.be/html/001maingeniaal2.htm<br /><br />http://www.msnucleus.org/membership/html/k-6/rc/minerals/3/rcm3_1a.html<br /><br />Regular geometric shapes do occur in geology as well as biology. It does seem positively amazing to some when they discover naturally formed crystals in regular geometric shapes. Man's tendency to anthropomorphize or see mystical significance in things has attached importance to crystal shapes despite centuries of science demonstrating that such attributions are without foundation.

 

[yevaud]

Mlorrey:<br /><br />Got that right. Casual relationships are just that. You can find them everywhere... <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[bonzelite]

i'm waiting for someone to take the bait of this thread. <br /><br />

 

[silylene old]

<font color="yellow">So, if you are presented with an irregular object and you wish to determine what its boundaries are, what is a good way of going about it? How do you prevent or at least detect the human tendency to see things which are not there (pareidolia)? If two or more lines appear equally likely for a given edge, how do you choose between them? And most importantly, how do you do this in a way which is reliable and which others can duplicate consistently? </font><br /><br />Calli, there are whole books and journals dedicated to this subject. The Journal of the Society of Photoimaging Engineers (SPIE) has published about a dozen articles on this subject every month for the last 20 years. I know about this because I have published quite a few articles in SPIE (although in a different area of imaging science).<br /><br />A quick google of "edge detection SPIE" picks up 318,000 references and the first fifty at least looked highly relevent.<br /><br />Picking out geometric figures is a highly developed mathematical subject with many algorithms, imaging tools and data manipulations. It is of high technological and military importance because it has everything to do with image recognition for MRI's, artifical vision, remotely-piloted vehicles, and for computer-aided image analysis from spy satellites. The articles within the J SPIE often show high altitude photographs and then illustrate algorithms which identify roads, airfields, planes, tanks, cars, ships and even people - with many examples and photos (the journal is rather interesting even to a layman). The algorithms can pick out geometric figures and then assess the probability that these figures are correctly identified. <br /><br />For example, any of the 100+ references cited here could be pertinent to this discussion of identifying geometric figures from satellite observations:<br />http://iris.usc.edu/Visio <div class="Discussion_UserSignature"> <div class="Discussion_UserSignature" align="center"><em><font color="#0000ff">- - - - - - - - - - - - - - - - - - - - - -</font></em> </div><div class="Discussion_UserSignature" align="center"><font color="#0000ff"><em>I really, really, really miss the "first unread post" function.</em></font> </div> </div>

 

[dragon04]

I like consistent and recurring symmetries in a pattern. Most architects do too, I think.<br /><br />I think I'd like specific and <b> exact </b> alignments. Like the way the Egyptians, Aztecs, Mayans, Stonehenge builders, etc aligned their constructions with regard to celestial objects. All vastly different cultures but working under the same principles.<br /><br />With eroded/obstructed objects, it does get problematic. Not so much with an array of such objects in proximity to one another, though, because I'd be back to looking for a system of exact symmetries between those objects.<br /><br />I'd also be looking for ratios... 1:4:9 and equilateral, isocoles, and right triangles come to mind. Ground penetrating radar and magnetometers? would also be something to build a body of evidence.<br /><br />But here is where we depart from absolute fact and move into the world of conjecture and speculation. Regardless of planetary origin, the only definitive way to prove or disprove an intelligently designed and constructed object or array of objects is relegated back to good old Archaeology.<br /><br />I'm more than willing to say that Feature X on the surface of Titan is interesting and worth further investigation, but to state an artificially constructed origin is the answer without some up close and personal investigation is not good science.<br /><br />What is "inferred" is not neccessarily what "is". With a good enough camera, for example, you can tell that the Great Wall is indeed a great wall from space. It is a consistent width over great distance and the towers are at regular interval. Again. A pattern of symmetry.<br /><br />The devil is in the details. Some structures, such as a canal, with proper resolution can easily be identified as an artificial waterway. Lowell's and Schiaparelli's canals were "revelations". SOmeone lived on Mars. An entire culture grew out of it.<br /><br />Then we had a good look. No canals. <br /><br />I'm not an expert in these disciplines like many of <div class="Discussion_UserSignature"> <em>"2012.. Year of the Dragon!! Get on the Dragon Wagon!".</em> </div>

 

[JonClarke]

To test for specific alignments you would have to invoke some sort of null hypothesis test, that a particular configuration is due to chance. This is widely used in biology.<br /><br />Jon <div class="Discussion_UserSignature"> <p><em>Whether we become a multi-planet species with unlimited horizons, or are forever confined to Earth will be decided in the twenty-first century amid the vast plains, rugged canyons and lofty mountains of Mars</em>  Arthur Clarke</p> </div>

 

[bonzelite]

<font color="orange"><br />I think to determine an artificial construct, it must pass the most exacting scrutiny and meet all criteria under vigorous attack. Even if that means waiting 100 years for real people to go dig it out. </font><br /><br />i agree.

 

[yevaud]

And that's it, Jon. The assumption with many of these, err, <i>highly speculative</i> ideas and lines of reasoning is that they <i>must</i> be correct. <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[silylene old]

Correct Yevaud.<br /><br />As I mentioned in my post, scientists and mathematicians have already come up with very good statistically sound algorithms for finding geometric patterns in aerial photography and then testing their validity. Such algorithms can determine the probability that a geometric figure is actually real, or just noise, or just an unremarkable juxtaposition of random objects. This isn't my area of expertise - but I do know it is an area of expertise, complete with journals, books, scientists and engineers working full time at it. As such, scientifically sound, statistically sound investigations could be done of the arial photographs, instead of endless non-expert speculations on this forum.<br /><br />I would suggest that a geometric-figure proponent take their pictures to a discussion board which is active with members who are SPIE image analysts, and see if you can enroll one of the experts to study your pictures.<br /><br />Maxtheknife, do you want me to find such a board for you to take your questions? <div class="Discussion_UserSignature"> <div class="Discussion_UserSignature" align="center"><em><font color="#0000ff">- - - - - - - - - - - - - - - - - - - - - -</font></em> </div><div class="Discussion_UserSignature" align="center"><font color="#0000ff"><em>I really, really, really miss the "first unread post" function.</em></font> </div> </div>

 

[mlorrey]

Quite so, silylene. In regards to the claim that we should look for golden ratios, this is bunk. For instance, the distances between the peaks of Mt Washington, NH, Mt Mansfield and Mt Ascutney in Vermont form an equilateral triangle, which the mystical Geomancers seem to attach significance to: <br /><br />http://www.geomancy.org/ezines/ezine_5/ezine_5b.html<br /><br />This sort of stuff is exactly the problem: you can find geometric relationships all through nature, from the smallest structures, such as salt flat or tundra evaporation crack patterns (my cousin published an article on this particular topic) up to mountain ranges, etc. With the Earth being spherical, and molecules and crystals forming geometric shapes, it is only to be expected that natural structures can assume apparently regular features.<br /><br />Basalt pillars are one of my favorite: they are quite regular six sided cylindrical rocks that form together in large formations, often resulting in the larger formations assuming similar proportions. They have even been used as building materials (such as one particular Maori city of ancient times), stacked like logs into structures, yet real scientists did not see significance in their regularity, only in that they were later used in a place and a way that defies a natural explaination.

 

[harmonicaman]

Here's a simple test to determine how good you really are at figuring out what a geometric object is when you're confronted with limited or incomplete information. Size isn't an issue, but how you believe the <i>Top View</i> of this object should appear is an indication of your geometric perception and spacial intuition!<br /><br /><b>The Test:</b><br /><br />Below is an unknown solid object shown in a <i>Side View</i> and a <i>Front View.</i> On a piece of paper, sketch the probable <i>Top View</i> of this object.<br /><br /><big>Side View:</big><br /><br /><b>000000000000000000000000<br />000000000000000000000000<br />000000000000000000000000<br />000000000000000000<br />000000000000000000<br />000000000000000000<br />000000000000000000000000<br />000000000000000000000000<br />000000000000000000000000</b><br /><br /><br /><big>Front View:</big><br /><br /><b>000000000000000000000000<br />000000000000000000000000<br />000000000000000000000000<br />0000XXXXXXXXXXXXXXXX0000<br />0000XXXXXXXXXXXXXXXX0000<br />0000XXXXXXXXXXXXXXXX0000<br />000000000000000000000000<br />000000000000000000000000<br />000000000000000000000000</b> <br /><br />I'll post some typical solutions later with a critique of what they may reveal about your problem solving abilities and logic skills... <img src="/images/icons/rolleyes.gif" /><br /><br />Enjoy!<br /><br />

 

[yevaud]

It would be a complete square, 24 long * 24 wide.<br /><br />(when I say "24," I mean "0's" of course). <br /><br />Edit: I presume you intended for anyone to answer this? Didn't mean to intrude, if not.<br /><br />Edit: by the way, the above answer is based on the information you provided. It doesn't mean other shapes are precluded. <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[JonClarke]

.I can think of three, possibly four solutions right away!<br /><br />Jon <div class="Discussion_UserSignature"> <p><em>Whether we become a multi-planet species with unlimited horizons, or are forever confined to Earth will be decided in the twenty-first century amid the vast plains, rugged canyons and lofty mountains of Mars</em>  Arthur Clarke</p> </div>

 

[harmonicaman]

<b>Yevaud -</b> Be careful! Are you <i>sure</i> your "Square" is the best solution???<br /><br /><b>JonClark -</b> Yes! There are several "Correct" solutions, but some are more elegant (or logical) than others. The solution you come up with reveals a bit about how your brain deals with completing geometric patterns from incomplete sets of information!

 

[yevaud]

Of course not. There could be an indentation or indentations on the opposite side, rear, bottom, and top, which can't be determined by the orthographic views shown.<br /><br />The square is one of many possibles, just a projection based on the information provided.<br /><br />Which is to say (your point, I believe) that a correct answer about something's geometry can't usually be determined given such scanty visual data.<br /><br />(I did take Engineering Drawing and Design Tech. courses, back when it was all drawing board and Vellum) <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[JonClarke]

I visualise this as three "planks" stacked above each other, top to bottom, A B C. I have raised the number of possible solutions to 6.<br /><br />Solution 1: A and C are square, B shortened on one side, resulting in the "slot" in the side view. Top looks square<br /><br />Solution 2: A and B as in solution 1, C a left-handed right angled triangle. Top triangle over reactangle over square<br /><br />Solution 3: A and B as in solution 1, C a right-handed right angled triangle. Top triangle over reactangle over square<br /><br />Solution 4: C and B as in solution 1, A a left-handed right angled triangle. looks square<br /><br />Solution 5: C and B as in solution 1, A a right-handed right angled triangle. Top looks square<br /><br />Solution 6: A B & C equilateral triangles, B has the apex cut off. Top view an equilateral triangle.<br /><br />Jon <div class="Discussion_UserSignature"> <p><em>Whether we become a multi-planet species with unlimited horizons, or are forever confined to Earth will be decided in the twenty-first century amid the vast plains, rugged canyons and lofty mountains of Mars</em>  Arthur Clarke</p> </div>

 

[harmonicaman]

<b>Yevaud & JonClarke -</b><br /><br />Wow! You guys are putting a lot of thought into this, I'm impressed! Jon; are the clues that indicate this is triangular object really there?<br /><br />Here's how the "Square" solution appears in a <i>Top View</i> (Rows of Os omitted to show squareness):<br /><br /><big>Top View:</big><br /><br /><b>000000000000000000000000<br />000000000000000000000000<br />000000000000000000000000<br />000000000000000000000000<br />000000000000000000000000<br />000000000000000000000000<br />000000000000000000000000<br />000000000000000000000000<br />000000000000000000000000<br />000000000000000000000000<br />000000000000000000000000<br />0<u>00</u>00<u>00</u>00<u>00</u>00<u>00</u>00<u>00</u>00<u>00</u>0<br />000000000000000000000000<br />000000000000000000000000<br />000000000000000000000000</b><br /><br /><br />Does this accurately account for the <i>Front View</i>? (Note that the Xs don't go all the way across the <i>Front View</i> as they would appear to do in the "Square" solution...)

 

[yevaud]

It *can* be the top view, but not neccessarily. For example, given the two views we have to work from:<br /><br />----------------- Rear ----------------<br /><br /><br /><b>000|000000000000000000|000<br />000|000000000000000000|000<br />000|000000000000000000|000<br />000|000000000000000000|000<br />000|000000000000000000|000<br />000|000000000000000000|000<br />000|000000000000000000|000<br />0000000000000000000000000<br />0000000000000000000000000<br />0000000000000000000000000<br />000|000000000000000000|000<br />000|000000000000000000|000<br />000|000000000000000000|000<br />000|000000000000000000|000<br />000|000000000000000000|000</b><br /><br /><br />---------------- Front ----------------<br /><br />For example, you can see that there is the notch apparently cut into the front of the object. But there could equally be one in the rear, and we wouldn't know it. Not enough views. <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[yevaud]

Or, for example, there could be the following on the Right side, and as with other possibles, we wouldn't know.<br /><br />---------------- Rear -----------------<br /><br /><b>000000000000000000000000<br />000000000000000000000000<br />00000000000000000<br />000000000000000000000000<br />000000000000000000000000<br />00000000000000000<br />00000000000000000<br />000000000000000000000000<br />00000000000000000<br />000000000000000000000000<br />000000000000000000000000<br />00000000000000000<br />00000000000000000<br />000000000000000000000000<br />000000000000000000000000</b><br /><br />--------------- Front -------------- <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[harmonicaman]

<b>Yevaud -</b><br /><br />But you are adding elements to the object that are not actually indicated in the two views! <br /><br />Isn't this exactly the same kind of thing as seeing trees or faces on Mars? <br /><br />You must not "Add" anything to the object that isn't logically indicated and create something that isn't really there!<br /><br />This process is more akin to stripping away everything you aren't sure about and only what is left and you are sure about can be included in the <i>Top View</i>.

 

[yevaud]

Not at all. With only two views, there may be any number of shapes we can't see.<br /><br />The difference between this and the FOM thread is the following:<br /><br />These are fairly tight geometric shapes, and you provided me with two views. Using the rules of Orthographic Projection and Geometry, I can be fairly certain when I state that a shape is *not* precluded here. But I also point out that there’s insufficient information to proceed, and so I have merely displayed a few of the possible shapes (among hundreds, I’m sure).<br /><br />In the FOM thread, several nondescript terrain features were related together geometrically. Note the particular word: <b>nondescript.</b> Many of the features used in that thread were, frankly, cherry-picked *because* they fell into a useful relationship with other equally random terrain features. And then these “relationships” were then used to indicate artificiality, and hence an ancient and sentient Martian civilization.<br /><br />In point of fact, I'm certain that a reanalysis of the pictures used in that thread would show that there are many, many terrain features present. Interesting that the only one's used are those that fall into a certain number of possibles. The rest were discarded.<br /><br />I think that says it as concisely as I possibly can.<br /> <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[vogon13]

Is there any way I could post this with out sounding snarky?<br /><br />Standards for detection of geometric shapes:<br /><br />Seems like a person who was invariably wrong about this sort of thing could find utility if those evaluating his (her) analysis was aware of the (consistent) fallibility.<br /><br /> <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>