YOLOv1

26 July 2020

Photo by Jess Barnett

Origin: You Only Look Once: Unified, Real-Time Object Detection

Abstract

• As a regression problem to spatially separated bounding boxes and associated class probabilities
• A single neural network predicts bounding boxes and class probabilities directly from full images in one evaluation
• more localization errors but is less likely to predict false positives on background

The YOLO Detection System

1. resizes the input image to 448 × 448
2. runs a single convolutional network on the image
3. thresholds the resulting detections bythe model’s confidence

The Model

Procedure

1. It divides the image into an S × S grid [448 × 448 -> 7 x 7]
       If the center of an object falls into a grid cell, that grid cell is responsible for detecting that object.
2. Each grid cell predicts B bounding boxes, confidence for those boxes, and C class probabilities.
       Bounding Box: x, y, w, h(center)
    Confidence: Pr(object)⋅IoUpredtruth
3. Final output tensor: S × S × (B ∗ 5 + C)

The Loss Function

λcoord ∑S2i=0∑Bj=01obj ij[(xi−ˆxi)2+(yi−ˆyi)2]+λcoord ∑S2i=0∑Bj=01obj ij[(√wi−√ˆwi)2+(√hi−√ˆhi)2]+∑S2i=0∑Bj=01obj ij(Ci−ˆCi)2+λnoobj ∑S2i=0∑Bj=01noobj ij(Ci−ˆCi)2+∑S2i=01obj i∑c∈ classes (pi(c)−ˆpi(c))2

        i: 0~(S2-1) [iterate each grid (0~48)]
        j: 0~(B-1) [iterate each bbox (0~1)]
1objij&1noobjij:[0000001000001000001000001000001000001000001000000][1111110111110111110111110111110111110111110111111]

        For 1objij, we have B predictions in each cell, only the one with largest IoU shall be labeled as 1

Coordinate Loss

λcoord ∑S2i=0∑Bj=01obj ij[(xi−ˆxi)2+(yi−ˆyi)2]+λcoord ∑S2i=0∑Bj=01obj ij[(√wi−√ˆwi)2+(√hi−√ˆhi)2]

• x, y: predicated bbox center
• w, h: predicated bbox width & height
• ˆx,ˆy: labeled bbox center
• ˆw,ˆh: labeled bbox width & height
• √w,√h: Suppress the effect for larger bbox
• λcoord : 5. because there’s only 8 dimensions. Too less comparing to other losses weighted loss essentially.

Confidence Loss

+∑S2i=0∑Bj=01objij(Ci−ˆCi)2+λnoobj ∑S2i=0∑Bj=01noobj ij(Ci−ˆCi)2

• ˆCi: confidence score [IoU] of predicted and ground truth
• Ci: preidcted confidence score [IoU] generated from network

Note:

• ˆCi is 0 or 1 integer
• λnoobj =0.5, because there’s so many non-object bboxes
• Train: confidence = Pr(object)⋅IoUpredtruth
• Test: individual box confidence predicton:
       confidence = Pr(clsiobj)Pr(obj)⋅IoUpredtruth

Classification loss

+S2∑i=01obji∑c∈ classes (pi(c)−ˆpi(c))2

Each cell will only predict 1 object, which is decided by the bbox with the largest IoU.

▶ Don't forget to do NMS after generating bboxes.

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The YOLOv1 Pros & Cons

Pros:

• one stage, really fast

Cons:

• Bad for crowed objects[1 cell 1 obj]
• Bad for small objects
• Bad for objects with new width-height ratio
• No BN