Point Cloud Classification

What kind of label could we have?

• stop sign
• person
• wall
• buildings, etc

Could M be just a matrix with size $N\times 7$, where $N$ is the number of points?

No, cuz the matrix encoding discards … see the slides

How to include all the dimensions in the analysis? Apparently Deep Learning

So we are looking for a function $M$ that outputs the class for point $p_i\in P$. Typically, it also depends on its neighborhood $N(p_i)$ ⇒ $M(p_i,N(i))=class$. How do I select the neighborhood? See the slides or research. I think I can do it with kNN.

Turning features into classes

Through affine transformations (linear). $y_1=A_{1}x+b_1$, $y_2=A_{2}x+b_2$, …

But linearity fails on non-linearity separable data. So we can just use $ReLU(x)=\max (0,x)$. I know from PointNet that the $\max$ function is symmetrical. It’s important to keep the invariant property.

You can stack ReLU functions to create a really complex approx function. Insert the slide with the triangle. Apparently, it’s a norm?

How to sample the neighborhood of a point?

Computational Efficiency is still a problem. The neighborhood selection can be done with the ball query idea from PointNet. What’s the fastest way to downsample down to K points? Apparently it’a combination of random sampling and attention mechanism. See “RandLA-Net: Efficient semantic segmentation of large-scale point clouds”.

There’s a drawback. What if you have 90% of ground in your point cloud? That’s what the attentive pooling is solving.

Receptive Field: all the data that was used to compute the features aggregations. With each layer, the receptive field grows. Research this concept more :)

READ THAT PAPER! Results are quite insane

Current models are only based on transformers.

See the possible exam questions.