*These are my personal notes from fast.ai course and will continue to be updated and improved if I find anything useful and relevant while I continue to review the course to study much more in-depth. Thanks for reading and happy learning!*

Move from single object to multi-object detection.

**Main focus**is on the single shot multibox detector (SSD).Multi-object detection by using a loss function that can combine losses from multiple objects, across both localization and classification.

Custom architecture that takes advantage of the difference receptive fields of different layers of a CNN.

YOLO v3

Simple but powerful trick called focal loss.

Must read

Focal Loss for Dense Object Detection (RetinaNet)

Additional papers (optional)

Understanding Anchors by fast.ai's fellow, Hiromi Suenaga

Stanford CS231n videos:

Coursera's deeplearning.ai course videos:

Other videos:

YOLO CVPR 2016 talk -- the idea of using grid cells and treating detection as a regression problem is focused on in more detail.

YOLOv2 talk -- there is some good information in this talk, although some drawn explanations are omitted from the video. What I found interesting was the bit on learning anchor boxes from the dataset. There's also the crossover with NLP at the end.

Visualization of SSD_MultiHead by Chloe Sultan (@chloews)

You should understand this by now:

Pathlib; JSON

Dictionary comprehensions

`defaultdict`

How to jump around fastai source

matplotlib Object Oriented API

Lambda functions

Bounding box coordinates

Custom head; bounding box regression

A classifier is anything with dependent variable is categorical or binomial. As opposed to regression which is anything with dependent variable is continuous. Naming is a little confusing but will be sorted out in future. Here, `continuous`

is `True`

because our dependent variable is the coordinates of bounding box — hence this is actually a regressor data.

tfms = tfms_from_model(f_model, sz, crop_type=CropType.NO, aug_tfms=augs)md = ImageClassifierData.from_csv(PATH, JPEGS, BB_CSV, tfms=tfms, continuous=True, bs=4)

**Data Augmentation**

augs = [RandomFlip(),RandomRotate(30),RandomLighting(0.1,0.1)]

tfms = tfms_from_model(f_model, sz, crop_type=CropType.NO, aug_tfms=augs)md = ImageClassifierData.from_csv(PATH, JPEGS, BB_CSV, tfms=tfms, continuous=True, bs=4)idx = 3fig, axes = plt.subplots(3, 3, figsize=(9, 9))for i, ax in enumerate(axes.flat):x, y = next(iter(md.aug_dl))ima = md.val_ds.denorm(to_np(x))[idx]b = bb_hw(to_np(y[idx]))print('b:', b)show_img(ima, ax=ax)draw_rect(ax, b)

b: [ 1. 89. 499. 192.]b: [ 1. 89. 499. 192.]b: [ 1. 89. 499. 192.]b: [ 1. 89. 499. 192.]b: [ 1. 89. 499. 192.]b: [ 1. 89. 499. 192.]b: [ 1. 89. 499. 192.]b: [ 1. 89. 499. 192.]b: [ 1. 89. 499. 192.]

As you can see, the image gets rotated and lighting varies, but bounding box is not moving and is in a wrong spot [00:06:17]. This is the problem with data augmentations when your dependent variable is pixel values or in some way connected to the independent variable — they need to be augmented together.

The dependent variable needs to go through all the geometric transformation as the independent variables.

To do this [00:07:10], every transformation has an optional `tfm_y`

parameter:

augs = [RandomFlip(tfm_y=TfmType.COORD),RandomRotate(30, tfm_y=TfmType.COORD),RandomLighting(0.1,0.1, tfm_y=TfmType.COORD)]tfms = tfms_from_model(f_model, sz, crop_type=CropType.NO, aug_tfms=augs, tfm_y=TfmType.COORD)md = ImageClassifierData.from_csv(PATH, JPEGS, BB_CSV, tfms=tfms, continuous=True, bs=4)

`TrmType.COORD`

indicates that the `y`

value represents coordinate. This needs to be added to all the augmentations as well as `tfms_from_model`

which is responsible for cropping, zooming, resizing, padding, etc.

idx = 3fig, axes = plt.subplots(3, 3, figsize=(9, 9))for i, ax in enumerate(axes.flat):x, y = next(iter(md.aug_dl))ima = md.val_ds.denorm(to_np(x))[idx]b = bb_hw(to_np(y[idx]))print(b)show_img(ima, ax=ax)draw_rect(ax, b)

[ 1. 60. 221. 125.][ 0. 12. 224. 211.][ 0. 9. 224. 214.][ 0. 21. 224. 202.][ 0. 0. 224. 223.][ 0. 55. 224. 135.][ 0. 15. 224. 208.][ 0. 31. 224. 182.][ 0. 53. 224. 139.]

**custom_head**

`learn.summary()`

will run a small batch of data through a model and prints out the size of tensors at every layer. As you can see, right before the `Flatten`

layer, the tensor has the shape of 512 by 7 by 7. So if it were a rank 1 tensor (i.e. a single vector) its length will be 25088 (512 * 7 * 7)and that is why our custom header's input size is 25088. Output size is 4 since it is the bounding box coordinates.

We combine the two to create something that can classify and localize the largest object in each image.

There are 3 things that we need to do to train a neural network:

Data

Architecture

Loss function

We need a `ModelData`

object whose independent variable is the images, and dependent variable is a tuple of bounding box coordinates and class label.

There are several ways to do this, but here's a particularly 'lazy' and convenient way that is to create two `ModelData`

objects representing the two different dependent variables we want: 1. bounding boxes coordinates 2. class

f_model=resnet34sz=224bs=64# Split dataset for validation setval_idxs = get_cv_idxs(len(trn_fns))tfms = tfms_from_model(f_model, sz, crop_type=CropType.NO, tfm_y=TfmType.COORD, aug_tfms=augs)

`ModelData`

for bounding box of the largest object:

md = ImageClassifierData.from_csv(PATH, JPEGS, BB_CSV, tfms=tfms,bs=bs, continuous=True, val_idxs=val_idxs)

`ModelData`

for classification of the largest object:

md2 = ImageClassifierData.from_csv(PATH, JPEGS, CSV, tfms=tfms_from_model(f_model, sz))

Let's break that down a bit.

CSV_FILES = PATH / 'tmp'!ls {CSV_FILES}bb.csv lrg.csv

`BB_CSV`

is the CSV file for bounding boxes of the largest object. This is simply a regression with 4 outputs (predicted values). So we can use a CSV with multiple 'labels'.

!head -n 10 {CSV_FILES}/bb.csvfn,bbox008197.jpg,186 450 226 496008199.jpg,84 363 374 498008202.jpg,110 190 371 457008203.jpg,187 37 359 303000012.jpg,96 155 269 350008204.jpg,144 142 335 265000017.jpg,77 89 335 402008211.jpg,181 77 499 281008213.jpg,125 291 166 330

`CSV`

is the CSV file for large object classification. It contains the CSV data of image filename and class of the largest object (from annotations JSON).

!head -n 10 {CSV_FILES}/lrg.csvfn,cat008197.jpg,car008199.jpg,person008202.jpg,cow008203.jpg,sofa000012.jpg,car008204.jpg,person000017.jpg,horse008211.jpg,person008213.jpg,chair

A **dataset** can be anything with `__len__`

and `__getitem__`

. Here's a dataset that adds a second label to an existing dataset:

class ConcatLblDataset(Dataset):"""A dataset that adds a second label to an existing dataset."""def __init__(self, ds, y2):"""Initializeds: contains both independent and dependent variablesy2: contains the additional dependent variables"""self.ds, self.y2 = ds, y2def __len__(self):return len(self.ds)def __getitem__(self, i):x, y = self.ds[i]# returns an independent variable and the combination of two dependent variables.return (x, (y, self.y2[i]))

We'll use it to add the classes to the bounding boxes labels.

trn_ds2 = ConcatLblDataset(md.trn_ds, md2.trn_y)val_ds2 = ConcatLblDataset(md.val_ds, md2.val_y)

Here is an example dependent variable:

# Grab the two 'label' (bounding box & class) from a record in the validation dataset.val_ds2[0][1] # record at index 0. labels at index 1, input image(x) at index 0 (we are not grabbing this)

(array([ 0., 1., 223., 178.], dtype=float32), 14)

We can replace the dataloaders' datasets with these new ones.

md.trn_dl.dataset = trn_ds2md.val_dl.dataset = val_ds2

We have to `denorm`

alize the images from the dataloader before they can be plotted.

idx = 9x, y = next(iter(md.val_dl)) # x is image array, y is labelsima = md.val_ds.ds.denorm(to_np(x))[idx] # reverse the normalization done to a batch of images.b = bb_hw(to_np(y[0][idx]))b

array([134., 148., 36., 48.])

Plot image and object bounding box.

ax = show_img(ima)draw_rect(ax, b)draw_text(ax, b[:2], md2.classes[y[1][idx]])

Let's break that code down a bit.

Inspect

`y`

variable:

print(f'type of y: {type(y)}, y length: {len(y)}')print(y[0].size()) # bounding box top-left coord & bottom-right coord valuesprint(y[1].size()) # object category (class)# -----------------------------------------------------------------------------# Output# -----------------------------------------------------------------------------type of y: <class 'list'>, y length: 2torch.Size([64, 4])torch.Size([64])

# y[0] returns 64 set of bounding boxes (labels).# Here's we only grab the first 2 images' bounding boxes. The returned data type is PyTorch FloatTensor in GPU.print(y[0][:2])# Grab the first 2 images' object classes. The returned data type is PyTorch LongTensor in GPU.print(y[1][:2])# -----------------------------------------------------------------------------# Output# -----------------------------------------------------------------------------0 1 223 1787 123 186 194[torch.cuda.FloatTensor of size 2x4 (GPU 0)]143[torch.cuda.LongTensor of size 2 (GPU 0)]

Inspect

`x`

variable:data from GPU

x.size() # batch of 64 images, each image with 3 channels and size of 224x224# -----------------------------------------------------------------------------# Output# -----------------------------------------------------------------------------torch.Size([64, 3, 224, 224])data from CPU

to_np(x).shape# -----------------------------------------------------------------------------# Output# -----------------------------------------------------------------------------(64, 3, 224, 224)

The architecture will be the same as the one we used for the classifier and bounding box regression, but we will just combine them. In other words, if we have `c`

classes, then the number of activations we need in the final layer is 4 plus `c`

. 4 for bounding box coordinates and `c`

probabilities (one per class).

We'll use an extra linear layer this time, plus some dropout, to help us train a more flexible model. In general, we want our custom head to be capable of solving the problem on its own if the pre-trained backbone it is connected to is appropriate. So in this case, we are trying to do quite a bit — classifier and bounding box regression, so just the single linear layer does not seem enough.

If you were wondering why there is no `BatchNorm1d`

after the first `ReLU`

, ResNet backbone already has `BatchNorm1d`

as its final layer.

head_reg4 = nn.Sequential(Flatten(),nn.ReLU(),nn.Dropout(0.5),nn.Linear(25088, 256),nn.ReLU(),nn.BatchNorm1d(256),nn.Dropout(0.5),nn.Linear(256, 4 + len(cats)))models = ConvnetBuilder(f_model, 0, 0, 0, custom_head=head_reg4)learn = ConvLearner(md, models)learn.opt_fn = optim.Adam

Inspect what's inside `cats`

:

print(type(cats))print(len(cats))print('%s, %s' % (cats[1], cats[2]))# -----------------------------------------------------------------------------# Output# -----------------------------------------------------------------------------<class 'dict'>20aeroplane, bicycle

The loss function needs to look at these `4 + len(cats)`

activations and decide if they are good — whether these numbers accurately reflect the position and class of the largest object in the image. We know how to do this. For the first 4 activations, we will use L1Loss just like we did before (L1Loss is like a Mean Squared Error — instead of sum of squared errors, it uses sum of absolute values). For rest of the activations, we can use cross entropy loss.

def detn_loss(input, target):"""Loss function for the position and class of the largest object in the image."""bb_t, c_t = target# bb_i: the 4 values for the bbox# c_i: the 20 classes `len(cats)`bb_i, c_i = input[:, :4], input[:, 4:]bb_i = F.sigmoid(bb_i) * 224 # scale bbox values to stay between 0 and 224 (224 is the max img width or height)bb_l = F.l1_loss(bb_i, bb_t) # bbox lossclas_l = F.cross_entropy(c_i, c_t) # object class loss# I looked at these quantities separately first then picked a multiplier# to make them approximately equalreturn bb_l + clas_l * 20def detn_l1(input, target):"""Loss function for the first 4 activations.L1Loss is like a Mean Squared Error — instead of sum of squared errors, it uses sum of absolute values"""bb_t, _ = targetbb_i = input[:, :4]bb_i = F.sigmoid(bb_i) * 224return F.l1_loss(V(bb_i), V(bb_t)).datadef detn_acc(input, target):"""Accuracy"""_, c_t = targetc_i = input[:, 4:]return accuracy(c_i, c_t)

`input`

: activations.`target`

: ground truth.`bb_t, c_t = target`

: our custom dataset returns a tuple containing bounding box coordinates and classes. This assignment will destructure them.`bb_i, c_i = input[:, :4]`

,`input[:, 4:]`

: the first`:`

is for the batch dimension. e.g.: 64 (for 64 images).`b_i = F.sigmoid(bb_i) * 224`

: we know our image is 224 by 224.`Sigmoid`

will force it to be between 0 and 1, and multiply it by 224 to help our neural net to be in the range of what it has to be.

:question: **Question:** As a general rule, is it better to put BatchNorm before or after ReLU [00:18:02]?

Jeremy would suggest to put it after a ReLU because BatchNorm is meant to move towards zero-mean one-standard deviation. So if you put ReLU right after it, you are truncating it at zero so there is no way to create negative numbers. But if you put ReLU then BatchNorm, it does have that ability and gives slightly better results. Having said that, it is not too big of a deal either way. You see during this part of the course, most of the time, Jeremy does ReLU then BatchNorm but sometimes does the opposite when he wants to be consistent with the paper.

:question: **Question:** What is the intuition behind using dropout after a BatchNorm? Doesn't BatchNorm already do a good job of regularizing [00:19:12]?

BatchNorm does an okay job of regularizing but if you think back to part 1 when we discussed a list of things we do to avoid overfitting and adding BatchNorm is one of them as is data augmentation. But it's perfectly possible that you'll still be overfitting. One nice thing about dropout is that is it has a parameter to say how much to drop out. Parameters are great specifically parameters that decide how much to regularize because it lets you build a nice big over parameterized model and then decide on how much to regularize it. Jeremy tends to always put in a drop out starting with p=0 and then as he adds regularization, he can just change the dropout parameter without worrying about if he saved a model he want to be able to load it back, but if he had dropout layers in one but no in another, it will not load anymore. So this way, it stays consistent.

Now we have out inputs and targets, we can calculate the L1 loss and add the cross entropy [00:20:39]:

bb_l = F.l1_loss(bb_i, bb_t)clas_l = F.cross_entropy(c_i, c_t)return bb_l + clas_l * 20

This is our loss function. Cross entropy and L1 loss may be of wildly different scales — in which case in the loss function, the larger one is going to dominate. In this case, Jeremy printed out the values and found out that if we multiply cross entropy by 20, that makes them about the same scale.

learn.crit = detn_losslearn.metrics = [detn_acc, detn_l1]# Set learning rate and trainlr = 1e-2learn.fit(lr, 1, cycle_len=3, use_clr=(32, 5))# -----------------------------------------------------------------------------# Output# -----------------------------------------------------------------------------epoch trn_loss val_loss detn_acc detn_l10 71.055205 48.157942 0.754 33.2026511 51.411235 39.722549 0.776 26.3636262 42.721873 38.36225 0.786 25.658993[array([38.36225]), 0.7860000019073486, 25.65899333190918]

It is nice to print out information as you train, so we grabbed L1 loss and added it as metrics.

learn.save('reg1_0')learn.freeze_to(-2)lrs = np.array([lr/100, lr/10, lr])learn.fit(lrs/5, 1, cycle_len=5, use_clr=(32, 10))# -----------------------------------------------------------------------------# Output# -----------------------------------------------------------------------------epoch trn_loss val_loss detn_acc detn_l10 36.650519 37.198765 0.768 23.8658141 30.822986 36.280846 0.776 22.7436292 26.792856 35.199342 0.756 21.5643843 23.786961 33.644777 0.794 20.6260754 21.58091 33.194585 0.788 20.520627[array([33.19459]), 0.788, 20.52062666320801]

learn.unfreeze()learn.fit(lrs/10, 1, cycle_len=10, use_clr=(32, 10))# -----------------------------------------------------------------------------# Output# -----------------------------------------------------------------------------epoch trn_loss val_loss detn_acc detn_l10 19.133272 33.833656 0.804 20.7742981 18.754909 35.271939 0.77 20.5720072 17.824877 35.099138 0.776 20.4942963 16.8321 33.782667 0.792 20.1391324 15.968 33.525141 0.788 19.8489045 15.356815 33.827995 0.782 19.4832426 14.589975 33.49683 0.778 19.5312917 13.811117 33.022376 0.794 19.4629078 13.238251 33.300647 0.794 19.4238689 12.613972 33.260653 0.788 19.346758[array([33.26065]), 0.7880000019073486, 19.34675830078125]

A detection accuracy is in the low 80's which is the same as what it was before. This is not surprising because ResNet was designed to do classification so we wouldn't expect to be able to improve things in such a simple way. It certainly wasn't designed to do bounding box regression. It was explicitly actually designed in such a way to not care about geometry — it takes the last 7 by 7 grid of activations and averages them all together throwing away all the information about where everything came from.

Interestingly, when we do accuracy (classification) and bounding box at the same time, the L1 seems a little bit better than when we just do bounding box regression [00:22:46].

:memo: If that is counterintuitive to you, then this would be one of the main things to think about after this lesson since it is a really important idea.

**The big idea** is this — figuring out what the main object in an image is, is kind of the hard part. Then figuring out exactly where the bounding box is and what class it is is the easy part in a way. So when you have a single network that's both saying what is the object and where is the object, it's going to share all the computation about finding the object. And all that shared computation is very efficient. When we back propagate the errors in the class and in the place, that's all the information that is going to help the computation around finding the biggest object. So anytime you have multiple tasks which share some concept of what those tasks would need to do to complete their work, it is very likely they should share at least some layers of the network together. Later, we will look at a model where most of the layers are shared except for the last one.

Here are the result [00:24:34]. As before, it does a good job when there is single major object in the image.

We want to keep building models that are slightly more complex than the last model so that if something stops working, we know exactly where it broke.

Global scope variables:

PATH = Path('data/pascal')trn_j = json.load((PATH / 'pascal_train2007.json').open())IMAGES, ANNOTATIONS, CATEGORIES = ['images', 'annotations', 'categories']FILE_NAME, ID, IMG_ID, CAT_ID, BBOX = 'file_name', 'id', 'image_id', 'category_id', 'bbox'cats = dict((o[ID], o['name']) for o in trn_j[CATEGORIES])trn_fns = dict((o[ID], o[FILE_NAME]) for o in trn_j[IMAGES])trn_ids = [o[ID] for o in trn_j[IMAGES]]JPEGS = 'VOCdevkit/VOC2007/JPEGImages'IMG_PATH = PATH / JPEGS

Define common functions.

Very similar to the first Pascal notebook, a model (single object detection).

def hw_bb(bb):# Example, bb = [155, 96, 196, 174]return np.array([ bb[1], bb[0], bb[3] + bb[1] - 1, bb[2] + bb[0] - 1 ])def get_trn_anno():trn_anno = collections.defaultdict(lambda:[])for o in trn_j[ANNOTATIONS]:if not o['ignore']:bb = o[BBOX] # one bbox. looks like '[155, 96, 196, 174]'.bb = hw_bb(bb)trn_anno[o[IMG_ID]].append( (bb, o[CAT_ID]) )return trn_annotrn_anno = get_trn_anno()def show_img(im, figsize=None, ax=None):if not ax:fig, ax = plt.subplots(figsize=figsize)ax.imshow(im)ax.set_xticks(np.linspace(0, 224, 8))ax.set_yticks(np.linspace(0, 224, 8))ax.grid()ax.set_xticklabels([])ax.set_yticklabels([])return axdef draw_outline(o, lw):o.set_path_effects( [patheffects.Stroke(linewidth=lw, foreground='black'),patheffects.Normal()] )def draw_rect(ax, b, color='white'):patch = ax.add_patch(patches.Rectangle(b[:2], *b[-2:], fill=False, edgecolor=color, lw=2))draw_outline(patch, 4)def draw_text(ax, xy, txt, sz=14, color='white'):text = ax.text(*xy, txt, verticalalignment='top', color=color, fontsize=sz, weight='bold')draw_outline(text, 1)def bb_hw(a):return np.array( [ a[1], a[0], a[3] - a[1] + 1, a[2] - a[0] + 1 ] )def draw_im(im, ann):# im is image, ann is annotationsax = show_img(im, figsize=(16, 8))for b, c in ann:# b is bbox, c is class idb = bb_hw(b)draw_rect(ax, b)draw_text(ax, b[:2], cats[c], sz=16)def draw_idx(i):# i is image idim_a = trn_anno[i] # training annotationsim = open_image(IMG_PATH / trn_fns[i]) # trn_fns is training image file namesdraw_im(im, im_a) # im_a is an element of annotation

Setup.

MC_CSV = PATH / 'tmp/mc.csv'trn_anno[12]# -----------------------------------------------------------------------------# Output# -----------------------------------------------------------------------------[(array([ 96, 155, 269, 350]), 7)]mc = [ set( [cats[p[1]] for p in trn_anno[o] ] ) for o in trn_ids ]mcs = [ ' '.join( str(p) for p in o ) for o in mc ] # stringify mcprint('mc:', mc[1])print('mcs:', mcs[1])# -----------------------------------------------------------------------------# Output# -----------------------------------------------------------------------------mc: {'horse', 'person'}mcs: horse persondf = pd.DataFrame({ 'fn': [trn_fns[o] for o in trn_ids], 'clas': mcs }, columns=['fn', 'clas'])df.to_csv(MC_CSV, index=False)

:memo: One of the students pointed out that by using Pandas, we can do things much simpler than using `collections.defaultdict`

and shared this gist. The more you get to know Pandas, the more often you realize it is a good way to solve lots of different problems.

**Model**

Setup ResNet model and train.

f_model = resnet34sz = 224bs = 64tfms = tfms_from_model(f_model, sz, crop_type=CropType.NO)md = ImageClassifierData.from_csv(PATH, JPEGS, MC_CSV, tfms=tfms, bs=bs)learn = ConvLearner.pretrained(f_model, md)learn.opt_fn = optim.Adamlr = 2e-2learn.fit(lr, 1, cycle_len=3, use_clr=(32, 5))# -----------------------------------------------------------------------------# Output# -----------------------------------------------------------------------------epoch trn_loss val_loss <lambda>0 0.319539 0.139347 0.95351 0.172275 0.080689 0.97242 0.116136 0.075965 0.975[array([0.07597]), 0.9750000004768371]# Define learning rates to searchlrs = np.array([lr/100, lr/10, lr])# Freeze the model till the last 2 layers as beforelearn.freeze_to(-2)# Refit the modellearn.fit(lrs/10, 1, cycle_len=5, use_clr=(32, 5))# -----------------------------------------------------------------------------# Output# -----------------------------------------------------------------------------epoch trn_loss val_loss <lambda>0 0.071997 0.078266 0.97341 0.055321 0.082668 0.97372 0.040407 0.077682 0.97573 0.027939 0.07651 0.97564 0.019983 0.07676 0.9763[array([0.07676]), 0.9763000016212463]# Save the modellearn.save('mclas')learn.load('mclas')

**Evaluate the model**

y = learn.predict()x, _ = next(iter(md.val_dl))x = to_np(x)fig, axes = plt.subplots(3, 4, figsize=(12, 8))for i, ax in enumerate(axes.flat):ima = md.val_ds.denorm(x)[i]ya = np.nonzero(y[i] > 0.4)[0]b = '\n'.join(md.classes[o] for o in ya)ax = show_img(ima, ax=ax)draw_text(ax, (0, 0), b)plt.tight_layout()

Multi-class classification is pretty straight forward [00:28:28]. One minor tweak is the use of `set`

in this line so that each object type appear once:

mc = [ set( [cats[p[1]] for p in trn_anno[o] ] ) for o in trn_ids ]

Next up, **finding multiple objects in an image**.

We have an input image that goes through a conv net which outputs a vector of size `4 + c`

where `c = len(cats)`

. This gives us an object detector for a single largest object. Let's now create one that finds 16 objects. The obvious way to do this would be to take the last linear layer and rather than having `4 + c`

outputs, we could have `16 x (4+c)`

outputs. This gives us 16 sets of class probabilities and 16 sets of bounding box coordinates. Then we would just need a loss function that will check whether those 16 sets of bounding boxes correctly represented the up to 16 objects in the image (we will go into the loss function later).

The second way to do this is rather than using `nn.linear`

, what if instead, we took from our ResNet convolutional backbone and added an nn.Conv2d with stride 2 [00:31:32]? This will give us a `4 x 4 x [# of filters]`

tensor — here let's make it `4 x 4 x (4 + c)`

so that we get a tensor where the number of elements is exactly equal to the number of elements we wanted. Now if we created a loss function that took a `4 x 4 x (4 + c)`

tensor and and mapped it to 16 objects in the image and checked whether each one was correctly represented by these `4 + c`

activations, this would work as well. It turns out, both of these approaches are actually used [00:33:48]. The approach where the output is one big long vector from a fully connected linear layer is used by a class of models known as YOLO (You Only Look Once), where else, the approach of the convolutional activations is used by models which started with something called SSD (Single Shot Detector). Since these things came out very similar times in late 2015, things are very much moved towards SSD. So the point where this morning, YOLO version 3 came out and is now doing SSD, so that's what we are going to do. We will also learn about why this makes more sense as well.

**SSD Approach**

Let's imagine that we had another `Conv2d(stride=2)`

then we would have `2 x 2 x (4 + c)`

tensor. Basically, it is creating a grid that looks something like this:

This is how the geometry of the activations of the second extra convolutional stride 2 layer are.

What we might do here [00:36:09]? We want each of these grid cell (Conv quadrant) to be responsible for finding the largest object in that part of the image.

Why do we want each convolutional grid cell (quadrant) to be responsible for finding things that are in the corresponding part of the image? The reason is because of something called the receptive field of that convolutional grid cell. The basic idea is that throughout your convolutional layers, every piece of those tensors has a receptive field which means which part of the input image was responsible for calculating that cell. Like all things in life, the easiest way to see this is with Excel [00:38:01].

Take a single activation (in this case in the maxpool layer) and let's see where it came from [00:38:45]. In Excel you can do Formulas :arrow_right: Trace Precedents. Tracing all the way back to the input layer, you can see that it came from this 6 x 6 portion of the image (as well as filters).

**Example:**

If we trace one of the maxpool activation backwards:

Tracing back even farther until we get back to the source image:

What is more, the middle portion has lots of weights (or connections) coming out of where else, cells in the outside (edges) only have one (don't have many) weight coming out. In other words, the center of the box has more dependencies. So we call this 6 x 6 cells the receptive field of the one activation we picked.

*Note that the receptive field is not just saying it's this box but also that the center of the box has more dependencies [00:40:27].* This is **a critically important concept when it comes to understanding architectures and understanding why conv nets work the way they do**.

We're going to make a simple first model that simply predicts what object is located in each cell of a 4x4 grid. Later on we can try to improve this.

**Architecture**

The architecture is, we will have a ResNet backbone followed by one or more 2D convolutions (one for now) which is going to give us a `4x4`

grid.

# Build a simple convolutional modelclass StdConv(nn.Module):"""A combination block of Conv2d, BatchNorm, Dropout"""def __init__(self, nin, nout, stride=2, drop=0.1):super().__init__()self.conv = nn.Conv2d(nin, nout, 3, stride=stride, padding=1)self.bn = nn.BatchNorm2d(nout)self.drop = nn.Dropout(drop)def forward(self, x):return self.drop(self.bn(F.relu(self.conv(x))))def flatten_conv(x, k):bs, nf, gx, gy = x.size()x = x.permute(0, 2, 3, 1).contiguous()return x.view(bs, -1, nf//k)# This is an output convolutional model with 2 `Conv2d` layers.class OutConv(nn.Module):"""A combination block of `Conv2d`, `4 x Stride 1`, `Conv2d`, `C x Stride 1` with two layers.We are outputting `4 + C`"""def __init__(self, k, nin, bias):super().__init__()self.k = kself.oconv1 = nn.Conv2d(nin, (len(id2cat) + 1) * k, 3, padding=1) # +1 is adding one more class for background.self.oconv2 = nn.Conv2d(nin, 4 * k, 3, padding=1)self.oconv1.bias.data.zero_().add(bias)def forward(self, x):return [flatten_conv(self.oconv1(x), self.k),flatten_conv(self.oconv2(x), self.k)]

**The SSD Model**

class SSD_Head(nn.Module):def __init__(self, k, bias):super().__init__()self.drop = nn.Dropout(0.25)# Stride 1 conv doesn't change the dimension size, but we have a mini neural networkself.sconv0 = StdConv(512, 256, stride=1)self.sconv2 = StdConv(256, 256)self.out = OutConv(k, 256, bias)def forward(self, x):x = self.drop(F.relu(x))x = self.sconv0(x)x = self.sconv2(x)return self.out(x)head_reg4 = SSD_Head(k, -3.)models = ConvnetBuilder(f_model, 0, 0, 0, custom_head=head_reg4)learn = ConvLearner(md, models)learn.opt_fn = optim.Adam

SSD_Head:

We start with ReLU and dropout.

Then stride 1 convolution.

The reason we start with a stride 1 convolution is because that does not change the geometry at all— it just lets us add an extra layer of calculation. It lets us create not just a linear layer but now we have a little

**mini neural network**in our custom head.`StdConv`

is defined above — it does convolution, ReLU, BatchNorm, and dropout.*Most research code you see won't define a class like this, instead they write the entire thing again and again.*Don't be like that. Duplicate code leads to errors and poor understanding.Stride 2 convolution [00:44:56].

At the end, the output of step 3 is

`4x4`

which gets passed to`OutConv`

.`OutConv`

has two separate convolutional layers each of which is stride 1 so it is not changing the geometry of the input. One of them is of length of the number of classes (ignore`k`

for now and`+1`

is for "background" — i.e. no object was detected), the other's length is 4.Rather than having a single conv layer that outputs

`4 + c`

, let's have two conv layers and return their outputs in a list.This allows these layers to specialize just a little bit. We talked about this idea that when you have multiple tasks, they can share layers, but they do not have to share all the layers.

In this case, our two tasks of creating a classifier and creating bounding box regression share every single layers except the very last one.

At the end, we flatten out the convolution because Jeremy wrote the loss function to expect flattened out tensor, but we could totally rewrite it to not do that.

It is very heavily orient towards the idea of expository programming which is the idea that programming code should be something that you can use to explain an idea, ideally as readily as mathematical notation, to somebody that understands your coding method.

**How do we write a loss function for this?**

The loss function needs to look at each of these 16 sets of activations, each of which has **4 bounding box coordinates** and **categories + 1** — `c + 1`

class probabilities and decide if those activations are close or far away from the object which is the closest to this grid cell in the image. If nothing is there, then whether it is predicting background correctly. That turns out to be very hard to do.

**Matching Problem**

The loss function actually needs to take each object in the image and match them to a convolutional grid cell.

The loss function needs to take each of the objects in the image and match them to one of these convolutional grid cells to say "this grid cell is responsible for this particular object" so then it can go ahead and say "okay, how close are the 4 coordinates and how close are the class probabilities".

Here's our goal:

Our dependent variable looks like the one on the left, and our final convolutional layer is going to be `4 x 4 x (c + 1)`

in this case `c = 20`

. We then flatten that out into a vector. Our goal is to come up with a function which takes in a dependent variable and also some particular set of activations that ended up coming out of the model and returns a higher number if these activations are not a good reflection of the ground truth bounding boxes; or a lower number if it is a good reflection.

**Testing**

Do a simple test to make sure that model works.

x, y = next(iter(md.val_dl))x, y = V(x), V(y)

for i, o in enumerate(y):y[i] = o.cuda()learn.model.cuda()# -----------------------------------------------------------------------------# Output# -----------------------------------------------------------------------------Sequential((0): Conv2d(3, 64, kernel_size=(7, 7), stride=(2, 2), padding=(3, 3), bias=False)(1): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True)(2): ReLU(inplace)(3): MaxPool2d(kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), dilation=(1, 1), ceil_mode=False)(4): Sequential((0): BasicBlock((conv1): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)(bn1): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True)(relu): ReLU(inplace)(conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)(bn2): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True))(1): BasicBlock((conv1): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)(bn1): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True)(relu): ReLU(inplace)(conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)(bn2): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True))(2): BasicBlock((conv1): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)(bn1): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True)(relu): ReLU(inplace)(conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)(bn2): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True)))... ... ...... ... ...(8): SSD_Head((drop): Dropout(p=0.25)(sconv0): StdConv((conv): Conv2d(512, 256, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))(bn): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True)(drop): Dropout(p=0.1))(sconv2): StdConv((conv): Conv2d(256, 256, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1))(bn): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True)(drop): Dropout(p=0.1))(out): OutConv((oconv1): Conv2d(256, 21, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))(oconv2): Conv2d(256, 4, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1)))))

batch = learn.model(x)anchors = anchors.cuda()grid_sizes = grid_sizes.cuda()anchor_cnr = anchor_cnr.cuda()ssd_loss(batch, y, True)# -----------------------------------------------------------------------------# Output# -----------------------------------------------------------------------------0.40620.21800.13070.57620.15240.4794[torch.cuda.FloatTensor of size 6 (GPU 0)]0.1128[torch.cuda.FloatTensor of size 1 (GPU 0)]loc: 10.360502243041992, clas: 73.66346740722656Variable containing:84.0240[torch.cuda.FloatTensor of size 1 (GPU 0)]

x, y = next(iter(md.val_dl)) # grab a single batchx, y = V(x), V(y) # turn into variableslearn.model.eval() # set model to eval mode (trained in the previous block)batch = learn.model(x)b_clas, b_bb = batch # destructure the class and the bounding box

b_clas.size(), b_bb.size()# -----------------------------------------------------------------------------# Output# -----------------------------------------------------------------------------(torch.Size([64, 16, 21]), torch.Size([64, 16, 4]))

The dimension:

64 batch size by

16 grid cells

21 classes

4 bounding box coords

**Let's now look at the ground truth **`y`

**.**

We will look at image 7.

idx = 7b_clasi = b_clas[idx]b_bboxi = b_bb[idx]ima = md.val_ds.ds.denorm(to_np(x))[idx]bbox, clas = get_y(y[0][idx], y[1][idx])bbox, clas# -----------------------------------------------------------------------------# Output# -----------------------------------------------------------------------------(Variable containing:0.6786 0.4866 0.9911 0.62500.7098 0.0848 0.9911 0.54910.5134 0.8304 0.6696 0.9063[torch.cuda.FloatTensor of size 3x4 (GPU 0)], Variable containing:81017[torch.cuda.LongTensor of size 3 (GPU 0)])

*Note that the bounding box coordinates have been scaled to between 0 and 1.*

def torch_gt(ax, ima, bbox, clas, prs=None, thresh=0.4):"""We already have `show_ground_truth` function.This function simply converts tensors into numpy array. (gt stands for ground truth)"""return show_ground_truth(ax, ima, to_np((bbox * 224).long()),to_np(clas), to_np(prs) if prs is not None else None, thresh)

fig, ax = plt.subplots(figsize=(7, 7))torch_gt(ax, ima, bbox, clas)

The above is a ground truth.

Here is our 4x4 grid cells from our final convolutional layer.

fig, ax = plt.subplots(figsize=(7, 7))torch_gt(ax, ima, anchor_cnr, b_clasi.max(1)[1])

Each of these square boxes, different papers call them different things. The three terms you'll hear are: anchor boxes, prior boxes, or default boxes. We will stick with the term **anchor boxes**.

What we are going to do for this **loss function** is we are going to go through a **matching problem** where we are going to **take every one of these 16 boxes and see which one of these three ground truth objects has the highest amount of overlap with a given square**.

To do this, we have to have some way of measuring **amount of overlap** and a standard function for this is called **Jaccard index** (IoU).

`IoU = area of overlap / area of union`

We are going to go through and find the Jaccard overlap for each one of the three objects versus each of the 16 anchor boxes [00:57:11]. That is going to give us a `3x16`

matrix.

Here are the coordinates of all of our anchor boxes (center `x`

, center `y`

, height, width):

anchors# -----------------------------------------------------------------------------# Output# -----------------------------------------------------------------------------Variable containing:0.1250 0.1250 0.2500 0.25000.1250 0.3750 0.2500 0.25000.1250 0.6250 0.2500 0.25000.1250 0.8750 0.2500 0.25000.3750 0.1250 0.2500 0.25000.3750 0.3750 0.2500 0.25000.3750 0.6250 0.2500 0.25000.3750 0.8750 0.2500 0.25000.6250 0.1250 0.2500 0.25000.6250 0.3750 0.2500 0.25000.6250 0.6250 0.2500 0.25000.6250 0.8750 0.2500 0.25000.8750 0.1250 0.2500 0.25000.8750 0.3750 0.2500 0.25000.8750 0.6250 0.2500 0.25000.8750 0.8750 0.2500 0.2500[torch.cuda.FloatTensor of size 16x4 (GPU 0)]

Here are the amount of overlap between 3 ground truth objects and 16 anchor boxes:

Get the activations.

# a_ic: activations image cornersa_ic = actn_to_bb(b_bboxi, anchors)fig, ax = plt.subplots(figsize=(7, 7))# b_clasi.max(1)[1] -> object class id# b_clasi.max(1)[0].sigmoid() -> scale class probs using sigmoidtorch_gt(ax, ima, a_ic, b_clasi.max(1)[1], b_clasi.max(1)[0].sigmoid(), thresh=0.0)

**Calculate Jaccard index (all objects **`x`

** all grid cells)**

We are going to go through and find the Jaccard overlap for each one of the 3 ground truth objects versus each of the 16 anchor boxes. That is going to give us a `3x16`

matrix.

# Test ssd_1_loss logicoverlaps = jaccard(bbox.data, anchor_cnr.data)overlaps# -----------------------------------------------------------------------------# Output# -----------------------------------------------------------------------------Columns 0 to 90.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00910.0000 0.0000 0.0000 0.0000 0.0000 0.0000