In mathematics, the 'Haar wavelet' is a certain sequence of functions.

It describes a distribution of Haar wavelet responses within the interest point neighbourhood.

For features, it uses the sum of the Haar wavelet response around the point of interest.

The Walsh functions are related to the Haar wavelets; both form a complete orthogonal system.

The Haar wavelet is also the simplest possible wavelet.

They can be viewed as a soft variety of Haar wavelets whose shape is fine-tuned by two parameters and .

The Haar wavelet has several notable properties:

They owe their name to their intuitive similarity with Haar wavelets and were used in the first real-time face detector.

The earliest wavelets were based on expanding a function in terms of rectangular steps, the Haar wavelets.

The first wavelet of the Legendre's family is exactly the well-known Haar wavelet.

Based on sums of approximated 2D Haar wavelet responses and made efficient use of integral images.

The technical disadvantage of the Haar wavelet is that it is not continuous, and therefore not differentiable.

The Haar wavelet in Java (programming language):

A publication by Papageorgiou et al. discussed working with an alternate feature set based on Haar wavelets instead of the usual image intensities.

In her seminal paper, Daubechies derives a family of wavelets, the first of which is the Haar wavelet.

Viola and Jones adapted the idea of using Haar wavelets and developed the so-called Haar-like features.

As a special case of the Daubechies wavelet, the Haar wavelet is also known as D2.

The Haar measure, Haar wavelet, and Haar transform are named in his honor.

Ranklets achieve similar response to Haar wavelets as they share the same pattern of orientation-selectivity, multi-scale nature and a suitable notion of completeness.

Early work in time-frequency analysis can be seen in the Haar wavelets (1909) of Alfréd Haar, though these were not significantly applied to signal processing.

For an input represented by a list of numbers, the Haar wavelet transform may be considered to simply pair up input values, storing the difference and passing the sum.

See also a full list of wavelet-related transforms but the common ones are listed below: Mexican hat wavelet, Haar Wavelet, Daubechies wavelet, triangular wavelet.

The fourth tool in RODS implements a wavelet approach, which decomposes the time series using Haar wavelets, and uses the lowest resolution to remove long-term trends from the raw series.

Generalized Haar wavelets are oriented Haar wavelets, and were used in 2001 by Mohan, Papageorgiou, and Poggio in their own object detection experiments.

Adam7 is a multiscale model of the data, similar to a discrete wavelet transform with Haar wavelets, though it starts from an 8x8 block, and downsamples the image, rather than decimating (low-pass filtering, then downsampling).