Category: Uncategorized

This week I finished running a lot of tests and organized the result in the following doc.

https://docs.google.com/document/d/19wJg-HrnnUYyvSiVqkFE2jATxtm9D1kOiT-zvxu3zbk/edit?usp=sharing

The leaf curvature demo:

(With an issue of matplotlib, the latest plotted part is always on the top. So the part of the video seems like the leaf is rotating in another direction.)

And here is the comparsion between origin leaf and the curvature with two different window size:

The curvature with too small windows size is too local. The larger size shows better result. Should this be relevant to the size of the leaf? For the deliverable of leaf curvature, which kind of data, should we deliver a 2D matrix shows curvature of every points on each leaf, or just a statistic number to describe the leaf? I have done some search about this, it seems no general leaf curvature definition. Also the gaussian curvature and mean curvature version is on the way.

Leaf length and width

The merge process is running on Danforth server. Since both east and west sensor are processed. It is possible to using two data from same time and plot to evaluate our method.

I'm going to train some networks on the depth and reflect data, evaluate the length width pipeline and complete the curvature(if we figure out the method to delivery them.)

I made Npair loss and Proxy loss embedding method available on the Lilou: /pless_nfs/home/share_projects/

Leaf length/width pipeline

The leaf length/width pipeline for season 6 is running on DDPSC server. This is going to be finished in next week.

The pipeline currently running finds the leaves first instead of plots. So I rewrote the merging to fit this method.

Leaf Curvature

I'm digging into the PCL (Point Cloud Library) to see if we could apply this library to our point cloud data. This library is originally developed on C++. There is an official python binding project under development. But there are not too many activities on that repo for years. (Also there is a API for calculate the curvature is not implemented on this binding.) So should we working on some point cloud problems on C++? If we are going to keep working on the ply data, considering the processing speed for point cloud and the library, this seems like a appropriate and viable way to work with.

Or, at least for the curvature, I could implement the method used in PCL with python. Since we already have the xyz-map. Finding the neiberhood could be faster than on the ply file. Then the curvature could be calculated with some differential geometry methods

PCL: http://pointclouds.org/

PCL curvature: http://docs.pointclouds.org/trunk/group__features.html

Python bindings to the PCL: https://github.com/strawlab/python-pcl

Reverse Phenotyping

Since the ply data are too large (~20 TB) to download(~6 MB/s). I created a new pipeline to find only the cropping position with ply file. So that I can run this on NCSA server and use those information to crop the raw data on our server. This is running on NCSA server now and I'm working on the cropping procedure.

I'm going to try Triplet loss, Hong's NN loss and Magnet loss to train the new data and do what we did before to visualize the result.

This post has several purposes.

FIRST: We need a better name or acronym than yoked t-sne.  it kinda sucks.

1. Loosely Aligned t-Sne
2. Comparable t-SNE (Ct-SNE)?
3. t-SNEEZE? t-SNEs

SECOND: How can we "t-SNEEZE" many datasets at the same time?

Suppose you are doing image embedding, and you start from imagenet, then from epoch to epoch you learn a better embedding.  It might be interesting to see the evolution of where the points are mapped.  To do this you'd like to yoke (or align, or tie together, or t-SNEEZE) all the t-SNEs together so that they are comparable.

t-SNE is an approach to map high dimensional points to low dimensional points.  Basically, it computes the similarity between points in high dimension, using the notation:

P(i,j) is (something like) how similar point i is to point j in high dimensions --- (this is measured from the data), and

Q(i,j) is (something like) how similar point i is to point j in low dimension.

the Q(i,j) is defined based on where the 2-D points are mapped in the t-SNE plot, and the optimization finds 2-D points that makes Q and P as similar as possible.  Those points might be defined as (x(i), y(i)).

With "Yoked" t-SNE we have two versions of where the points go in high-dimesional space, so we have two sets of similarities.  So there is a P1(i,j) and a P2(i,j)

yoked t-SNE solves for points x1, y1 and x2,y2 so that the

1. Q1 defined by the x1, y1 points is similar to P1, and the
2. Q2 defined by the x2,y2 points are similar to P2 and the
3. x1,y1 points are similar to x2,y2

by adding this last cost (weight by something) to the optimization.  If we have *many* high dimensional points sets (e.g. P1, P2, ... P7, for perhaps large versions of "7") what can we do?

Idea 1: exactly implement the above approach, with steps 1...7 talking about how each embedding should have Q similar to P, and have step 8 penalize all pairwise distances between the x,y embeddings for each point.

Idea 2: (my favorite?).  The idea of t-SNE is to find which points are similar in high-dimensions and embed those close by.  I wonder if we can find all pairs of points that are similar in *any* embedding.  So, from P1... P7, make Pmax, so that Pmax(i,j) is the most i,j are similar in any high-dimensional space.  Then solve for each other embedding so that it has to pay a penalty to be different from Pmax?  [I think this is not quite the correct idea yet, but something like this feels right.  Is "Pmin" the thing we should use?]

 

Earlier this week, Dr. Pless, Abby and I worked through some of the derivations of the ellipse equations in order to better understand where our understanding of them may have gone awry. In doing so, I now believe there is a problem with the fact that we are not considering the direction of the surface normals of the glitter. It seems to me that this is the reason for the need for centroids to be scattered around the light/camera - this is how the direction of surface normals is seen by the equations; however, this is not realistically how our system is set up (we tend to have centroids all on one side of the light/camera).

I did the test of generating an ellipse, finding points on that ellipse, and then using my method of solving the linear equations to try and re-create the ellipse using just the points on the ellipse and their surface normals (which I know because I can find the gradient at any point on the ellipse, and the surface normal is the negative of the gradient).

Here are some examples of success when I generate an ellipse, find points on that ellipse (as well as their surface normals), and then try to re-create the ellipse:

 

Funny story - the issue of using all points on one side of the ellipse and it not working doesn't seem to be an issue anymore. Not sure whether this is a good thing or not yet...look for updates in future posts about this!

We decided to try and tackle the optimization approach and try to get that up and running for now, both in 2D and 3D. I am optimizing for both the light and the camera locations simultaneously.

Error Function

In each iteration of the optimization, I am computing the surface normals of each centroid using the current values of the light and camera locations. I then want to maximize the sum of the dot products of the actual surface normals and the calculated surface normals at each iteration. Since I am using a minimization function, I want to minimize the negative of the sum of dot products.

error = -1*sum(dot(GT_surf_norms, calc_surf_norms, 2));

2D Results

Initial Locations: [15, 1, 15, 3] (light_x, light_y, camera_x, camera_y)
I chose this initialization because I wanted to ensure that both the light & camera start on the correct side of the glitter, and are generally one above the other, since I know that this is their general orientation with respect to the glitter.

Final Locations: [25, 30, 25, 10]
Actual Locations: [25, 10, 25, 30]
Final Error: 10

So, the camera and light got flipped here, which sensibly could happen because there is nothing in the error function to ensure that they don't get flipped like that.

3D Results

Coming soon!

Other things I am thinking about in the coming days/week

1. I am not completely abandoning the beautiful ellipse equations that I have been working with. I am going to take some time to analyze the linear equations. One thing I will try to understand is whether there is variation in just 1 axis (what we want) or more than 1 axis (which would tell us that there is ambiguity in the data I am using when trying to define an ellipse).
2. After I finish writing up the optimization simulations in both 2D and 3D, I will also try to analyze the effect that some noise in the surface normals may have on the results of the optimization.

The problem of common metric loss(triplet loss, contrast divergence and N-pair loss)

For a group of images belong to a same class, these loss functions will randomly sample 2 images from the group and force their dot-product to be large/euclidean distance to be small. And finally, their embedding points will be clustered in to circle shape. But in fact this circle shape is a really strong constraints to the embedding. There should be a more flexibility for them to be clustered such as star shape and strip shape or a group image in several clusters.

Nearest Neighbor Loss

I design a new loss to loss the 'circle cluster' constraints. First, using the idea in the end of N-pair loss: constructing a batch of images with N class and each class contain M images.

1 finding the same label pair

When calculating the similarity for image i, label c, in the batch, I first find its nearest neighbor image with label c as the same label pair.

2.set the threshold for the same pair.

if the nearest neighbor image similarity is small than a threshold, then I don't construct the pair.

3.set the threshold for the diff pair.

With the same threshold, if the diff label image have similarity smaller than the threshold than it will not be push away.

T-SNE result