At inference time, an anchor-box-based object detection model follows a multi-step prediction pipeline for each input image. First, the model generates multiple anchor boxes at various positions and scales across the image. Next, it predicts a class label and a set of bounding-box offsets for every anchor box simultaneously. The predicted offsets are then applied to adjust the positions and sizes of the corresponding anchor boxes, producing a set of predicted bounding boxes. Finally, a filtering step retains only those predicted bounding boxes that satisfy certain criteria (such as confidence thresholds or non-maximum suppression), which are output as the final detections.

Object Detection Prediction Pipeline Using Anchor Boxes

To assign ground-truth bounding boxes to anchor boxes, we use an iterative algorithm based on their Intersection over Union (IoU). Given $$n_a$$ anchor boxes and $$n_b$$ ground-truth bounding boxes (where $$n_a \geq n_b$$), we compute a matrix $$\mathbf{X} \in \mathbb{R}^{n_a 	imes n_b}$$ where each element $$x_{ij}$$ is the IoU between anchor box $$A_i$$ and ground-truth box $$B_j$$. First, we find the largest element in $$\mathbf{X}$$, assign the corresponding ground-truth box to the anchor box, and discard its entire row and column. We repeat this process of finding the largest remaining element and discarding its row and column until all $$n_b$$ ground-truth boxes are assigned. Finally, we evaluate the remaining $$n_a - n_b$$ unassigned anchor boxes, assigning each to the ground-truth box with the highest IoU in its row, provided that this maximum IoU is strictly greater than a predefined threshold.

Ground-Truth Bounding Box Assignment to Anchor Boxes

To illustrate anchor box labeling, consider an image containing ground-truth bounding boxes for a dog and a cat, alongside a set of five generated anchor boxes, denoted as $$A_0, \ldots, A_4$$. The labeling process evaluates the pairs of anchor boxes and ground-truth bounding boxes based on Intersection over Union (IoU). For example, if the IoU between anchor box $$A_4$$ and the cat's ground-truth bounding box is the largest among all pairs, $$A_4$$ is labeled as the cat. Removing all pairs containing $$A_4$$ or the cat's bounding box, if the remaining pair with the largest IoU is $$A_1$$ and the dog's bounding box, $$A_1$$ is labeled as the dog. For the remaining unlabeled anchor boxes (e.g., $$A_0, A_2, A_3$$), they are assigned to the ground-truth bounding box with the highest IoU only if that IoU exceeds a predefined threshold (e.g., $$0.5$$). Thus, if $$A_2$$ has an IoU with the cat exceeding the threshold, it is labeled as the cat; conversely, if $$A_0$$ and $$A_3$$ have maximum IoUs below the threshold, they are labeled as the background class.

Anchor Box Labeling Example

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.

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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.

Anchor Box in Object Detection

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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

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.

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