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Add KaTeX support + updates to YOLOv9 model page (#8531)

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Co-authored-by: Glenn Jocher <glenn.jocher@ultralytics.com>
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docs/en/models/yolov9.md
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@ -58,12 +58,12 @@ The performance of YOLOv9 on the [COCO dataset](../datasets/detect/coco.md) exem
**Table 1. Comparison of State-of-the-Art Real-Time Object Detectors**
| Model | Parameters (M) | FLOPs (G) | APval 50:95 (%) | APval 50 (%) | APval 75 (%) | APval S (%) | APval M (%) | APval L (%) |
|----------|----------------|-----------|-----------------|--------------|--------------|-------------|-------------|-------------|
| YOLOv9-S | 7.2 | 26.7 | 46.8 | 63.4 | 50.7 | 26.6 | 56.0 | 64.5 |
| YOLOv9-M | 20.1 | 76.8 | 51.4 | 68.1 | 56.1 | 33.6 | 57.0 | 68.0 |
| YOLOv9-C | 25.5 | 102.8 | 53.0 | 70.2 | 57.8 | 36.2 | 58.5 | 69.3 |
| YOLOv9-E | 58.1 | 192.5 | 55.6 | 72.8 | 60.6 | 40.2 | 61.0 | 71.4 |
| Model | size<br><sup>(pixels) | AP<sup>val<br>50-95 | AP<sup>val<br>50 | AP<sup>val<br>75 | params<br><sup>(M) | FLOPs<br><sup>(B) |
|----------|:---------------------:|:-------------------:|:----------------:|:----------------:|:------------------:|:-----------------:|
| YOLOv9-S | 640 | 46.8 | 63.4 | 50.7 | 7.2 | 26.7 |
| YOLOv9-M | 640 | 51.4 | 68.1 | 56.1 | 20.1 | 76.8 |
| YOLOv9-C | 640 | 53.0 | 70.2 | 57.8 | 25.5 | 102.8 |
| YOLOv9-E | 640 | 55.6 | 72.8 | 60.6 | 58.1 | 192.5 |
YOLOv9's iterations, ranging from the smaller S variant to the extensive E model, demonstrate improvements not only in accuracy (AP metrics) but also in efficiency with a reduced number of parameters and computational needs (FLOPs). This table underscores YOLOv9's ability to deliver high precision while maintaining or reducing the computational overhead compared to prior versions and competing models.
@ -72,7 +72,7 @@ Comparatively, YOLOv9 exhibits remarkable gains:
- **Lightweight Models**: YOLOv9-S surpasses the YOLO MS-S in parameter efficiency and computational load while achieving an improvement of 0.4∼0.6% in AP.
- **Medium to Large Models**: YOLOv9-M and YOLOv9-E show notable advancements in balancing the trade-off between model complexity and detection performance, offering significant reductions in parameters and computations against the backdrop of improved accuracy.
The YOLOv9-C model, in particular, highlights the effectiveness of the architecture's optimizations. It operates with 42% fewer parameters and 21% less computational demand than YOLOv7 AF, yet it achieves comparable accuracy, demonstrating YOLOv9's significant efficiency improvements. Furthermore, the YOLOv9-E model sets a new standard for large models, with 15% fewer parameters and 25% less computational need than YOLOv8-X, alongside a substantial 1.7% improvement in AP.
The YOLOv9-C model, in particular, highlights the effectiveness of the architecture's optimizations. It operates with 42% fewer parameters and 21% less computational demand than YOLOv7 AF, yet it achieves comparable accuracy, demonstrating YOLOv9's significant efficiency improvements. Furthermore, the YOLOv9-E model sets a new standard for large models, with 15% fewer parameters and 25% less computational need than [YOLOv8x](yolov8.md), alongside a substantial 1.7% improvement in AP.
These results showcase YOLOv9's strategic advancements in model design, emphasizing its enhanced efficiency without compromising on the precision essential for real-time object detection tasks. The model not only pushes the boundaries of performance metrics but also emphasizes the importance of computational efficiency, making it a pivotal development in the field of computer vision.