An anchor box centered on a pixel of an image with height $$h$$ and width $$w$$ is parameterized by two quantities: a scale $$s \in (0, 1]$$ and an aspect ratio $$r > 0$$, defined as the ratio of the box's width to its height. Given these parameters, the width of the anchor box is $$ws\sqrt{r}$$ and the height is $$hs/\sqrt{r}$$. This formulation ensures that larger scales produce bigger boxes and that the aspect ratio controls the elongation of the box — values of $$r > 1$$ yield wider boxes, while values of $$r < 1$$ yield taller boxes. Since the scale is expressed relative to the image dimensions, the resulting anchor box dimensions are directly proportional to the image size.

Anchor Box Parameterization by Scale and Aspect Ratio

The multibox_prior function returns anchor box coordinates in a normalized form, where the $$x$$-axis values are divided by the image width and the $$y$$-axis values are divided by the image height. This means all coordinate values fall within the range $$[0, 1]$$, making them independent of the absolute pixel dimensions of the input image. Each anchor box is stored as four values representing the upper-left $$(x, y)$$ corner and the lower-right $$(x, y)$$ corner in this normalized coordinate system. To recover the original pixel coordinates for tasks such as visualization, a scaling tensor bbox_scale of the form $$(w, h, w, h)$$ is element-wise multiplied with the normalized coordinates to restore them to the image's native resolution.

Normalized Anchor Box Coordinates

In an object detection training dataset, every generated anchor box is treated as an individual training example. To train the model effectively, each anchor box must be assigned two specific types of supervision labels: a class label and an offset label. These labels are derived from the closest ground-truth bounding box assigned to the anchor box. Together, these labels provide the necessary signals for the model to simultaneously predict object categories and refine the bounding box coordinates.

Labeling Anchor Boxes in Training Data

The region proposal network (RPN) is an internal component of Faster R-CNN that generates region proposals by processing CNN-extracted feature maps in four steps. First, a $$3 	imes 3$$ convolutional layer with a padding of $$1$$ transforms the feature maps into a new output with $$c$$ channels, providing a length-$$c$$ feature vector for each spatial unit. Second, multiple anchor boxes of varying scales and aspect ratios are generated and centered on each pixel. Third, these length-$$c$$ feature vectors are used to predict a binary class (object or background) and a bounding box for each anchor box. Finally, non-maximum suppression is applied to the bounding boxes predicted as objects to remove overlapping results, yielding the final region proposals required by the region of interest pooling layer.

Region Proposal Network

An anchor box (also called a prior box) is a predefined bounding box that is centered on every pixel of an input image and serves as a candidate region for detecting objects. Rather than searching for objects at arbitrary positions and sizes, an object detection model generates a fixed set of anchor boxes with varying shapes across the entire image and then predicts how each anchor should be adjusted to tightly fit nearby objects. Each anchor box is fully determined once its center position, scale, and aspect ratio are specified. Anchor boxes provide the initial spatial hypotheses that a detector refines, enabling efficient coverage of potential ground-truth bounding boxes without exhaustive search.

Claude

In object detection, a bounding box is utilized to describe the precise spatial location of a target object within an image. Unlike simple image classification, object detection requires localizing the objects, which is generally achieved by defining a rectangular boundary that perfectly encapsulates the item of interest. These boundaries are plotted on an image coordinate system where the origin $$(0, 0)$$ is situated at the upper-left corner, with the positive $$x$$-axis extending horizontally to the right and the positive $$y$$-axis extending vertically downward.

Bounding Box in Object Detection

Dive into Deep Learning

In object detection, a bounding box is often represented by the coordinates of its upper-left and lower-right corners. Specifically, the box is determined by the $$x$$ and $$y$$ coordinates of the upper-left corner and the corresponding $$x$$ and $$y$$ coordinates of the lower-right corner within the image.

Two-Corner Bounding Box Representation

In object detection, an alternative bounding box representation uses the $$(x, y)$$-axis coordinates of the bounding box's center point, along with the overall width and height of the box.

Center-Width-Height Bounding Box Representation

To visually verify the accuracy of object detection models, bounding boxes can be drawn directly onto images using plotting libraries like `matplotlib`. Since plotting libraries often require specific input formats—such as the $$(x, y)$$ coordinates of the upper-left corner paired with the width and height of the rectangle—a programmatic helper function is typically used to convert the standard bounding box representation into the appropriate format for drawing the rectangular patches. This allows for a clear visual confirmation that the predicted boxes align with the main outlines of the target objects.

Visualizing Bounding Boxes

In deep learning frameworks, when working with multiple bounding boxes, they are programmatically represented as a two-dimensional tensor of shape $$(n, 4)$$. In this structural configuration, $$n$$ represents the total number of bounding boxes, while the dimension of size $$4$$ holds the numerical parameters defining each box, such as the two corner coordinates or the center position paired with width and height.

Bounding Box Tensor Shape

Anchor Box in Object Detection

In object detection, the similarity between two bounding boxes is measured using their Jaccard index, which is commonly referred to as the intersection over union (IoU). Treating the pixel area of any bounding box as a set of pixels, the IoU is calculated as the ratio of their intersection area to their union area: $$J(\mathcal{A},\mathcal{B}) = \frac{|\mathcal{A} \cap \mathcal{B}|}{|\mathcal{A} \cup \mathcal{B}|}$$. The IoU value ranges from $$0$$ to $$1$$, where $$0$$ indicates that the bounding boxes have absolutely no overlap, and $$1$$ indicates that the two bounding boxes are exactly equal.

Learn Before

Related

Learn After