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<!DOCTYPE html>
<html>
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<meta charset="utf-8" />
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<section data-markdown
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<textarea data-template>
# Object Detection
## **Design of Autonomous Systems**
### csci 6907/4907-Section 86
### Prof. **Sibin Mohan**
---
autonomous vehicle uses sensory input devices
(cameras, radar and lasers)
---
autonomous vehicle uses sensory input devices
(cameras, radar and lasers)
<br>
<br>
**how** does it actually "perceive"?
---
perception involves not just identifying that an object exists, but also,
---
perception involves not just identifying that an object exists, but also,
|||
|:-----|:------|
|object **classification**| **what** is it?|
---
perception involves not just identifying that an object exists, but also,
|||
|:-----|:------|
|object **classification**| **what** is it?|
|object **localization** | **where** is it?|
||
---
consider a **camera**,
---
consider a **camera**,
||||
|:-----|:------|:------|
|object **classification**| **what** is it?|**recognizing** objects <br>(cars, traffic lights, pedestrians)|
|object **localization** | **where** is it?||
||
---
consider a **camera**,
||||
|:-----|:------|:------|
|object **classification**| **what** is it?|**recognizing** objects <br>(cars, traffic lights, pedestrians)|
|object **localization** | **where** is it?|generating **bounding boxes**|
||
---
consider a **camera**,
<img src="img/object/camera_bounding_boxes.gif" width="1400">
---
multiple **classes** of object detection and localization methods,
1. classical [**computer vision** methods](#computer-vision-methods)
2. [**deep-learning** based methods](#deep-learning-methods)
---
## Computer Vision Methods
---
### 1. [Histogram of Gradient Objects](https://medium.com/analytics-vidhya/a-gentle-introduction-into-the-histogram-of-oriented-gradients-fdee9ed8f2aa) (HOG)
---
### 1. Histogram of Gradient Objects (HOG)
- mainly used for face and image detection
---
### 1. Histogram of Gradient Objects (HOG)
- mainly used for face and image detection
- image ($width \times height \times channels$) → feature vector, length $n$
- $n$ → chosen by user
Note:
- convert the image to a feature vector
---
### 1. Histogram of Gradient Objects (HOG)
- mainly used for face and image detection
- image ($width \times height \times channels$) → feature vector, length $n$
- $n$ → chosen by user
- **histogram of gradients** → used as image "features"
---
HOG example
<img src="img/object/hog.webp" width="1300">
---
gradients are **important**
---
gradients are **important**
- check for **edges** and **corners** in image
- through **regions of intensity changes**
---
gradients are **important**
- check for **edges** and **corners** in image
- through **regions of intensity changes**
- often pack much more information than flat regions
---
### 2. [Scale Invariant Feature Transform](https://medium.com/@deepanshut041/introduction-to-sift-scale-invariant-feature-transform-65d7f3a72d40) (SIFT)
---
### 2. Scale Invariant Feature Transform (SIFT)
- extracting **distinctive invariant features** from images
---
### 2. Scale Invariant Feature Transform (SIFT)
- extracting **distinctive invariant features** from images
- **reliable matching** → between different **views** of an object or scene
---
### 2. Scale Invariant Feature Transform (SIFT)
- extracting **distinctive invariant features** from images
- **reliable matching** → between different **views** of an object or scene
- finds **keypoints** in an image that do not change
---
finds **keypoints** based on,
- scale
- rotation
- illumination
---
SIFT example
<img src="img/object/sift.png" width="1500">
---
- image recognition → matches individual features to **database**
- database → known objects
---
- image recognition → matches individual features to **database**
- database → known objects
- using a fast nearest-neighbor algorithm
---
SIFT → robustly identify objects
---
SIFT → robustly identify objects
while achieving **near real-time** performance
---
### 3. [Viola-Jones Detector](https://www.mygreatlearning.com/blog/viola-jones-algorithm/)
---
### 3. [Viola-Jones Detector]
- used to accurately identify and analyze **human faces**
---
### 3. [Viola-Jones Detector]
- used to accurately identify and analyze **human faces**
- mainly works with grayscale images
---
### 3. [Viola-Jones Detector]
- given an image → looks at many smaller subregions
---
### 3. [Viola-Jones Detector]
- given an image → looks at many smaller subregions
- tries to find a face → looking for **specific features in each subregion**
---
### 3. [Viola-Jones Detector]
- given an image → looks at many smaller subregions
- tries to find a face → looking for **specific features in each subregion**
- check many different positions and scales
- image can contain **many faces** of **various sizes**
---
uses **Haar-like features** to detect faces
> [Haar wavelets](https://en.wikipedia.org/wiki/Haar_wavelet) → sequence of rescaled “square-shaped” functions which together form a wavelet family or basis
---
Viola-Jones example
<img src="img/object/viola_jones.webp" width="1400">
---
[textbook](https://autonomy-course.github.io/textbook/autonomy-textbook.html#computer-vision-methods) has links to the actual papers
---
## Deep-Learning Methods
---
## Deep-Learning Methods
use **neural networks** → classification, regression, representation
---
### neural networks
---
### neural networks
inspiration from biological neuroscience
---
### neural networks
inspiration from biological neuroscience
- stacking artificial "neurons" into **layers**
---
### neural networks
inspiration from biological neuroscience
- stacking artificial "neurons" into **layers**
- "training" them to process data
---
### neural networks
inspiration from biological neuroscience
- stacking artificial neurons into **layers**
- "training" them to process data
<br>
<br>
"deep" → multiple layers (<scb>3</scb> to <scb>1000s</scb>) in the network
---
a brief detour... into **neural networks**
---
a brief detour... into **neural networks**
no way I can possibly speedrun all of neural networks in one class!
---
### computational graphs
---
### computational graphs
- representation of mathematical operations
- using **directed acyclic** graphs
---
### computational graphs
- representation of mathematical operations
- using **directed acyclic** graphs
- used by neural networks for computation
---
### computational graphs
| | |
|---|---|
| nodes can be **variables** or **functions** | <img src="img/yolo/graph0.png" width="500"> |
||
---
### computational graphs
| | |
|---|---|
| nodes can be **variables** or **functions** <br> edges represent **flow of data** | <img src="img/yolo/graph0.png" width="500"> |
||
---
### computational graphs
| | |
|---|---|
| nodes can be **variables** or **functions** <br> edges represent **flow of data** <br> leaf nodes → **inputs**/**parameters** | <img src="img/yolo/graph0.png" width="500"> |
||
---
### computational graphs
| | |
|---|---|
| nodes can be **variables** or **functions** <br> edges represent **flow of data** <br> leaf nodes → **inputs**/**parameters** <br> internal nodes → **operations** | <img src="img/yolo/graph0.png" width="500"> |
||
---
### computational graphs
| | |
|---|---|
| nodes can be **variables** or **functions** <br> edges represent **flow of data** <br> leaf nodes → **inputs**/**parameters** <br> internal nodes → **operations** | <img src="img/yolo/graph0.png" width="500"> |
||
computation **strictly** proceeds: inputs → outputs
---
consider a simple example...
---
consider a simple example...
- a _single_ neuron computes, $y = x_1 w_1 + x_2 w_2$
---
consider a simple example...
- a _single_ neuron computes, $y = x_1 w_1 + x_2 w_2$
- drawn as a graph
- two multiplciation nodes
- feeding into a summation node
---
consider a simple example...
- a _single_ neuron computes, $y = x_1 w_1 + x_2 w_2$
- drawn as a graph
- two multiplciation nodes
- feeding into a summation node
directed edges carry **values** forward and **gradients** backward
---
### neural networks are **precisely** such graphs
---
### neural networks are **precisely** such graphs
- many layers of _parameterized_ operations
---
### neural networks are **precisely** such graphs
- many layers of _parameterized_ operations
- every deep learning framework (_e.g.,_ PyTorch, TensorFlow, JAX)
---
### neural networks are **precisely** such graphs
- many layers of _parameterized_ operations
- every deep learning framework (_e.g.,_ PyTorch, TensorFlow, JAX)
- builds internal computation graphs
- traversed in **reverse** order
- compute gradients
---
### key insight
keep the following separate:
---
### key insight
keep the following separate:
|concern|description|
|------|-------|
| **data** | input values $\vec{x}$ fed to the network <br> (e.g., pixel values of an image) |
---
### key insight
keep the following separate:
|concern|description|
|------|-------|
| **data** | input values $\vec{x}$ fed to the network <br> (e.g., pixel values of an image) |
| **weight** | learnable parameters $\vec{w}$ <br> that network adjusts during training |
---
### key insight
keep the following separate:
|concern|description|
|------|-------|
| **data** | input values $\vec{x}$ fed to the network <br> (e.g., pixel values of an image) |
| **weight** | learnable parameters $\vec{w}$ <br> that network adjusts during training |
| **structures** | graph topology <br> which ops connect to which inputs |
||
---
### key insight
|concern|graphical example|
|------|-------|
| **data** <br> **weight** <br> **structures** | <img src="img/yolo/activation.png" width="1100">|
||
---
### separating data, weights, structure
---
### separating data, weights, structure
|concern|changes/static|
|------|-------|
| data | changes during **inference** |
---
### separating data, weights, structure
|concern|changes/static|
|------|-------|
| data | changes during **inference** |
| weight | changes during **training** |
---
### separating data, weights, structure
|concern|changes/static|
|------|-------|
| data | changes during **inference** |
| weight | changes during **training** |
| structures | stays **fixed** |
||
---
### neuron computation
<img src="img/yolo/neuron.png" width="700">
---
### neuron computation
| | |
|---|---|
| computes **weighted sum** of inputs | <img src="img/yolo/neuron.png" width="700"> |
||
---
### neuron computation
| | |
|---|---|
| computes **weighted sum** of inputs <br> with two inputs, $x_1$ and $x_2$ <br> corresponding weights $w_1$ and $w_2$ | <img src="img/yolo/neuron.png" width="700"> |
||
---
### neuron computation
| | |
|---|---|
| computes **weighted sum** of inputs <br> with two inputs, $x_1$ and $x_2$ <br> corresponding weights $w_1$ and $w_2$ <br> $$\sum x \times w = y$$ | <img src="img/yolo/neuron.png" width="700"> |
||
---
### neuron computation
| | |
|---|---|
| computes **weighted sum** of inputs <br> with two inputs, $x_1$ and $x_2$ <br> corresponding weights $w_1$ and $w_2$ <br> $$\sum x \times w = y$$ which is a **dot product** | <img src="img/yolo/neuron.png" width="700"> |
||
---
### neuron computation
| | |
|---|---|
| $$\sum x \times w = y$$ can be represented as **vectors** | <img src="img/yolo/neuron.png" width="700"> |
||
---
### neuron computation
| | |
|---|---|
| $$\sum x \times w = y$$ $$\begin{bmatrix}x_1 & x_2\end{bmatrix} \cdot \begin{bmatrix}w_1 \\ w_2\end{bmatrix} = y $$ | <img src="img/yolo/neuron.png" width="700"> |
||
---
### neuron computation
| | |
|---|---|
| $\sum x \times w = y$ <br><br> $\begin{bmatrix}x_1 & x_2\end{bmatrix} \cdot \begin{bmatrix}w_1 \\ w_2\end{bmatrix} = y$ <br><br> $\vec{x} \cdot \vec{w} = y$ | <img src="img/yolo/neuron.png" width="700"> |
||
---
### vector formulation is crucial
- enables efficient **parallel** computation
- on modern hardware (GPUs)
---
## vector formulation
- a full layer with $n$ input neurons
---
## vector formulation
- a full layer with $n$ input neurons
- represented as matrix multiplication:
$\mathbf{y} = \mathbf{W}\mathbf{x}$, where $\mathbf{W} \in \mathbb{R}^{m \times n}$
---
### linear regression computational graph
---
### linear regression computational graph
- simplest example of "learnable component"
---
### linear regression computational graph
- given → inputs $x_1$, $x_2$ with weights $w_1$,$w_2$
---
### linear regression computational graph
- given → inputs $x_1$, $x_2$ with weights $w_1$,$w_2$
$$\hat{y} = f(w_1, x_1) + g(w_2, x_2) = w_1 x_1 + w_2 x_2$$
---
### linear regression computational graph
- given → inputs $x_1$, $x_2$ with weights $w_1$,$w_2$
$$\hat{y} = f(w_1, x_1) + g(w_2, x_2) = w_1 x_1 + w_2 x_2$$
<img src="img/yolo/linear_graph.png" width="800">
---
### linear regression computational graph
|||
|------|------|
| <img src="img/yolo/linear_graph.png" width="500"> | multiplication nodes → $f$, $g$ |
---
### linear regression computational graph
|||
|------|------|
| <img src="img/yolo/linear_graph.png" width="500"> | multiplication nodes → $f$, $g$ <br> feeding into summation node → $\hat{y}$ |
---
### linear regression computational graph
|||
|------|------|
| <img src="img/yolo/linear_graph.png" width="500"> | multiplication nodes → $f$, $g$ <br> feeding into summation node → $\hat{y}$ <br> each quantity → has a **precise mathematical rule** |
---
### linear regression computational graph
|||
|------|------|
| <img src="img/yolo/linear_graph.png" width="500"> | multiplication nodes → $f$, $g$ <br> feeding into summation node → $\hat{y}$ <br> each quantity → has a **precise mathematical rule** <br> every operation → **well-defined derivative**|
||
---
this is what makes **backpropagation** possible
---
<img src="img/yolo/update.png" width="1100">
Note:
- at some point we need to be able to send "feedback" to the neural net
---
### backpropagation
---
training a neural network...
---
training a neural network...
- finding weight values $\vec{w}$
---
training a neural network...
- finding weight values $\vec{w}$
- make network's outputs $\hat{y}$ match → ground-truth labels $y$
---
measure **mismatch** between outputs and ground-truths
---
mismatch measured via → **loss function**
---
mismatch measured via → **loss function**
$$\mathcal{L} = (y - \hat{y})^2$$
(mean square error)
---
### training
---
### training
- optimization problem
---
### training
- optimization problem
- minimise $\mathcal{L}$ over → weight space
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### training
- optimization problem
- minimise $\mathcal{L}$ over → weight space
- iteratively moving weights
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### training
- optimization problem
- minimise $\mathcal{L}$ over → weight space
- iteratively moving weights
- in the direction that **reduces loss**
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so we need a way to **update** the graph...
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so we need a way to **update** the graph...
...rather the **weights**
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### gradient descent | update rule
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### gradient descent | update rule
<img src="img/object/equations/pngs/equations-2.png" width="750">
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### gradient descent | update rule
<img src="img/object/equations/pngs/equations-3.png" width="1500">
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### "learning rate" | $LR$
- **step size** your algorithm takes
- trying to find _bottom_ of a hill
- point of **minimum error**
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### "learning rate" | $LR$
- **step size** your algorithm takes
- trying to find _bottom_ of a hill
- point of **minimum error**
<br>
<br>
typically very small positive number → $0.1-10^{-5}$
Note:
When a model is learning, it calculates which direction it needs to move to make fewer mistakes. The learning rate is the dial that controls how far it moves in that direction during each update. It is typically a very small positive number, often between $0.1$ and $10^{-5}$.
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### backpropagation | updating the graph
$$ \vec{w} = \vec{w} - LR \cdot \nabla L$$
<img src="img/yolo/update.png" width="1100">
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<img src="img/yolo/update.png" width="1100">
- key quantity → $\nabla \mathcal{L}$
- gradient of loss w.r.t. **every weight** in the network
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### multiplication → explicit
<img src="img/yolo/linear_alt.png" width="800">
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### "simplified"
<img src="img/yolo/linear_simple.png" width="800">
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### chain rule
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### chain rule
- backpropagation → efficient application of **chain rule**
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### chain rule
- backpropagation → efficient application of **chain rule**
- for a composition of functions, $f(x) = f(g(x))$:
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### chain rule
- backpropagation → efficient application of **chain rule**
- for a composition of functions, $f(x) = f(g(x))$:
$$\frac{\partial f}{\partial x} = \frac{\partial f}{\partial g}\frac{\partial g}{\partial x}$$
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### chain rule
- backpropagation → efficient application of **chain rule**
- for a composition of functions, $f(x) = f(g(x))$:
$$\frac{\partial f}{\partial x} = \frac{\partial f}{\partial g}\frac{\partial g}{\partial x}$$
<br>
<br>
but what does this mean..._in practice_?
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but what does this mean..._in practice_?
$$\frac{\partial f}{\partial x} = \frac{\partial f}{\partial g}\frac{\partial g}{\partial x}$$
---
but what does this mean..._in practice_?
$$\frac{\partial f}{\partial x} = \frac{\partial f}{\partial g}\frac{\partial g}{\partial x}$$
gradient flowing _back_ through a node equals...
---
but what does this mean..._in practice_?
$$\frac{\partial f}{\partial x} = \frac{\partial f}{\partial g}\frac{\partial g}{\partial x}$$
gradient flowing _back_ through a node equals...
<br>
gradient from _output_
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but what does this mean..._in practice_?
$$\frac{\partial f}{\partial x} = \frac{\partial f}{\partial g}\frac{\partial g}{\partial x}$$
gradient flowing _back_ through a node equals...
<br>
gradient from _output_ **$\times$** node's own _local derivative_
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but, why do we care about **derivatives**?
Note:
Imagine you are standing on a foggy mountain (representing the network's loss or error) and your goal is to get to the bottom (the lowest error possible). Because of the fog, you can't see the bottom.
Without derivatives, you'd have to take a step in a random direction, see if the altitude went down, and repeat. With millions of knobs, this would take forever.
The derivative tells you the exact slope of the ground right under your feet. By moving in the opposite direction of the gradient (gradient descent), you are guaranteed to be taking the most efficient step down the mountain.
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a derivative tells you → **exact slope** in front of you
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a derivative tells you → **exact slope** in front of you
we want to move in a direction **opposite** that of the gradient
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a derivative tells you → **exact slope** in front of you
we want to move in a direction **opposite** that of the gradient
<br>
<br>
### gradient **descent**
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### gradient descent and derivatives
- if a neural network is a giant machine
---