## Image Classification with Localization

In image classification with localization, we train a supervised algorithm to predict class as well as the bounding box around the object in the image. The term 'localization' refers to where the object is in the image. At Datalya, our deep learning consultants heavily rely on image classification with localization for computer vision projects.

To be specific, we feed an input image to a convolutional neural network, and it gives back a feature vector (fully connected layer). The feature vector is then injected into the softmax layer to get the prediction of a class. Let's say we are building an image classifier for self-driving car application with a set of four possible classes;

• $c_{1}$ pedestrian
• $c_{2}$ car
• $c_{3}$ motorcycle
• $c_{4}$ background

In this case, the softmax layer will have four units or outputs which come down to a standard image classification pipeline.

How about if we also have to localize objects in the image. For that softmax will have four addition output numbers, $b_{x}$, $b_{y}$, $b_{h}$, $b_{w}$, parameterizing the bounding box around the object.

Bounding box coordinates are defined according to following convention:

• upper left of image (0,0)
• lower right (1,1).
• middle point of bounding box defined by $b_{x}$, $b_{y}$
• width of bounding box $b_{w}$
• height of bounding box: $b_{h}$

In training set, each example contains not only class label but also four additional bounding box numbers ($b_{x}$, $b_{y}$, $b_{h}$, $b_{w}$). Now, our convolution neural network will learn to predict both class of object as well as its bounding box.

Target $y$: label vector will consist of 8 components;

• $p_{c}$: is there any object
• $b_{x}$: x coordinate of mid point of BB
• $b_{y}$: y coordinate of mid point of BB
• $b_{w}$: width of BB
• $b_{h}$: height of BB
• $c_{1}$: pedestrian
• $c_{2}$: car
• $c_{3}$: motorcycle

If images has a car and $c_{2}$ represents car class then $p_{c}$ and $c_{2}$ will be 1 and bounding box coordinates in $b_{x}$, $b_{y}$, $b_{w}$ and $b_{h}$.

If the image does not have an object in it, then $p_{c}$ will be 0, and the rest of the outputs to be '?' meaning "don't care."

The loss function to train a neural network for classification with localization would look like following;

$$\int(\hat{y}, y) = (\hat{y}_{1}- y_{1})^2 + (\hat{y}_{2}-y_{2})^2 + ... + (\hat{y}_{8} - y_{8})^2$$