This page judges this solution. It says where the solution is strong and where it breaks. It names the general ideas behind it. Then it places it beside the other five.
Contents#
- Where it is strong and where it breaks
- The general ideas behind this
- Where it sits among the other five
1. Where it is strong and where it breaks#
The earlier pages showed how the method works, so this section starts with how well it works. The examiner marked it over five blocks of 20 held-out arrangements. On the spaced arrangements it finds 100.0 glasses in every 100, in all five blocks. On the crowded arrangements it finds 73.0 in every 100, and the five blocks range from 70.3 to 75.5. The results puts these rows beside the other five solutions.
The strengths come first.
It can be read. Nothing is fitted. The rule is one sentence about distance on the table. Its one setting could be computed from two numbers the project already holds.
It is exact and repeatable. The same picture always gives the same groups. Nothing in the method is random or depends on an order.
When it fails, one printed number usually shows why. Each step gives one number worth printing: the pixels kept above the table, the squares marked, the groups found, the dots per group, and each group's width. For example, if the table height is set a little too low, the whole table top becomes one huge group. The count of kept pixels shows this at once. A grouping distance that is too small gives too many groups with too few dots. One that is too large gives too few groups, with one impossible width.
It gives places in real distances from the arm's base, because it works in the room from the start.
It fits the search for hidden glass. It already knows each found glass's place, width and height. So the arithmetic in looking again at what was hidden needs nothing more from it.
It has two weaknesses. One is a limit of the idea, and one is a limit of the sensor.
Someone has to be able to state the rule. Touching glasses leave no strip of bare table, so the rule cannot separate them. The case the rule cannot answer shows this. Two glasses one behind the other, at the same distance from the camera, also stay one group. And if all four kinds could be on the table at once, the range of allowed widths would be much wider. The width check would then be much weaker.
The rule needs depth readings, and real clear glass does not give them. Every dot in this method comes from a depth reading. A pixel with no reading gives nothing. The cell works only because the simulator draws the glasses as solid and opaque. What is on the table states this assumption. So this method would not work on real glasses as it stands. That is a limit of the method, not of the cell.
The next section shows that none of these ideas is new.
2. The general ideas behind this#
The strengths and weaknesses above come from well-known ideas, and this section names them. Together they are the standard recipe for an arm working over a table, and have been for about twenty years. Treat the depth picture as a cloud of points. Delete the table. Group what is left, one group per object. It became the default because it needs no training data, no model file, and no idea what the objects are. It also gives places in real distances, which an arm needs anyway.
The pinhole camera model — turning a pixel and a depth into a point#
The pinhole camera model is the simple camera model behind back-projection. Turning a pixel into a point in the room explains it. It goes wrong on surfaces a depth sensor reads badly, such as glass, polished metal or black plastic. There the depth is missing or wrong, so the points are wrong too.
For more, see the pinhole camera model, and Hartley and Zisserman's Multiple View Geometry.
Plane segmentation with RANSAC — finding and deleting the table#
RANSAC stands for random sample consensus (Fischler and Bolles, CACM, 1981). It fits a model to data that has many stray readings. For a table, it picks three points at random and makes the plane through them. It counts how many other points lie on that plane. It keeps the best plane after a few hundred tries. Deleting that plane leaves just the objects.
It works badly when no one shape fills most of the scene. It also works badly when the thing you want is the smaller part and several models fit equally well.
This solution does not need it. The table is fixed to the arm's frame, so its height is known. Finding it is a comparison, not a search. For more, see RANSAC.
Density-based clustering — grouping points by how close they are#
This is the grouping rule in grouping the dots by how close they are. Robotics calls it Euclidean cluster extraction. Its better-known relative in statistics is DBSCAN (Ester and others, KDD 1996). DBSCAN adds a rule that a point needs a minimum number of neighbours, so scattered noise cannot form a group. This solution keeps noise out more simply. It throws away any group with fewer than 100 dots. Like every rule of this kind, it cannot separate objects that touch.
For more, see DBSCAN and cluster analysis.
Least-squares shape fitting — turning a cloud of dots into a number#
This is the circle fit in checking a group against the widths the kind allows. It works badly on shapes the model does not describe. Then it returns a confident number, and only the residual would show the problem.
For more, Kåsa's circle fit and the Pratt and Taubin versions are the three standard forms. The geometry is in circular segment.
Visibility reasoning — knowing where you could not have looked#
A sensor's view splits space into three parts, not two. There is the part it saw something in, the part it saw nothing in, and the part it could not see at all. Treating the third part as the second is an easy mistake, because both look empty in the data. Mobile robots keep a map that marks each cell as free, occupied or unknown. This cell is a lucky case. The hidden part can be worked out exactly, because the glasses are upright round solids on a known plane. Looking again at what was hidden does that.
For more, see occupancy grid mapping.
These ideas explain the method on its own. The last section compares it with the other five solutions.
3. Where it sits among the other five#
This section uses everything above to place this solution among the six. It is the only one with no fitted numbers at all. Solution 3 also fits nothing in this cell, so it is closest in cost. But it still carries a weights file. The rule inside that file was fitted on someone else's photos for someone else's purpose. Nobody using it can say what the rule is. This solution's rule is one sentence, and that is the difference.
That makes it the baseline. The examiner keeps the input, the output and the marking the same for every solution. So a model's score can be compared with this one directly. The reading is simple: if a model cannot beat a written rule, it has gained nothing.
This solution also shows what the problem's promises are worth. Its rule exists only because of four promises. The glasses stand apart. The table's height is known. Only one kind is on the table at a time. The glasses give depth readings. A problem that a written rule can solve is a problem with generous promises. The other five are worth what they do when those promises break.
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