When processing collections of images in deep learning, it is common practice to read and represent a minibatch as a $$4^{	extrm{th}}$$-order tensor with the specific shape format of (batch size, number of channels, height, width). In this structure, the first dimension indexes the individual images within the batch, the second specifies the color channels (e.g., $$1$$ for grayscale images or $$3$$ for RGB), and the final two dimensions capture the spatial height and width.

Image Minibatch Tensor Dimensions

Building upon the representation of individual images, a dataset containing a collection or batch of multiple images is structured in code as a $$4^{\textrm{th}}$$-order tensor. In this data structure, the distinct, individual images within the collection are indexed along the newly added first axis, followed by the specific axes for height, width, and channels.

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In deep learning, a single color image is mathematically and programmatically represented as a $$3^{\textrm{rd}}$$-order tensor. The three distinct axes of this tensor correspond to the image's height, width, and color channels. At each spatial location defined by the height and width dimensions, the color intensities (such as red, green, and blue) are stacked along the channel axis.

Single Image Representation as a 3rd-Order Tensor

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Image Collection Representation as a 4th-Order Tensor

By convention in deep learning, an image is commonly stored as a $$c \times h \times w$$ tensor, where $$c$$ represents the number of color channels, $$h$$ is the height, and $$w$$ is the width. While grayscale images require only a single channel ($$c=1$$), modern color images typically use three channels (red, green, and blue). More complex data, such as hyperspectral imagery, can contain well over $$100$$ separate channels.

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