When generating anchor boxes with $$n$$ scales $$s_1, \ldots, s_n$$ and $$m$$ aspect ratios $$r_1, \ldots, r_m$$, using every possible $$(s_i, r_j)$$ combination at each pixel would produce $$whnm$$ total anchor boxes, which is computationally prohibitive. In practice, only those pairings that include either the first scale $$s_1$$ or the first aspect ratio $$r_1$$ are retained:

$$(s_1, r_1), (s_1, r_2), \ldots, (s_1, r_m), (s_2, r_1), (s_3, r_1), \ldots, (s_n, r_1)$$

This yields $$n + m - 1$$ distinct anchor boxes per pixel and $$wh(n + m - 1)$$ anchor boxes for the entire image, dramatically reducing the computational burden while still providing sufficient shape diversity to cover most ground-truth objects.

Practical Scale-Ratio Combination Strategy for Anchor Boxes

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.

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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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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.

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