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Kalman Filters and Hough Transforms Serve Different Estimation Tasks

Article Quant Q&A · Author: pyCthon
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Summary

The document compares two methods from robotics and computer vision and cautions that they address different tasks. A Hough transform detects shapes or objects from observations; it can support tracking, but the answer describes it as lacking a prediction step. A Kalman filter alternates between prediction and measurement updates, estimating hidden state variables such as velocity in a dynamic system.

The answer says Kalman filtering assumes linear system dynamics with Gaussian noise and is not suited to multimodal distributions. It also contrasts computational scaling, describing Hough transform cost as exponential and Kalman filter cost as quadratic in state space, without defining the precise setup behind those claims. The discussion points toward finance applications of Kalman filters but provides no trading method, empirical comparison, or detailed implementation guidance. Its main lesson is to choose based on the estimation problem and model assumptions rather than treating the methods as direct substitutes.

Key ideas

  • Hough transforms detect shapes or objects from observed data and do not inherently predict future state.
  • Kalman filters combine prediction and measurement updates to estimate hidden dynamic-system variables.
  • The described Kalman filter assumes linear dynamics and Gaussian noise.
  • The answer cautions that Kalman filters are unsuitable for multimodal distributions and gives only a broad computational comparison.

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StatisticsMachine learning
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# Kalman Filter Vs Hough Transform


# Kalman Filter Vs Hough Transform












These questions are in regards to the Kalman filter and the Hough Transform.

What are the Pros and Cons of using each method?

In what situations is it better to prefer one over the other?

## Answer by rtybase (score 4, accepted)

https://quant.stackexchange.com/a/3046

I am not sure they are comparable as they serve for slightly different purposes. In robotics (specifically vision), Hough Transform is used for objects (or shape) detection. This can subsequently be used for objects tracking, but Hough Transform has no prediction phase. On the other hand, Kalman Filter is a two phase algorithm; measure and predict. With dynamic systems it can be used to find/predict "hidden" parameters like velocity and respectively predict the next move that subsequently can be adjusted with the measurement phase. However, Kalman Filter assumes that the system's dynamic is linear, though with some Gaussian noise.

What else? Algorithm efficiency with regards to state space: exponential for Hough Transform and quadratic for Kalman Filter. And Kalman Filter (as far as I know) isn't applicable to multi-modal distribution cases.

Some useful links http://www.ptgrey.com/newsletters/images/GreShaJas04.pdf a work based on Hough Transform with with few complains: "Currently, the BHT does not include any predictive techniques. While predictive techniques such as Kalman filtering do not respond well to arbitrary motions, they may improve precision" and "The benefits of predictive techniques, such as Kalman and particle filtering, will also be investigated".

And closer to finance one http://www.r-bloggers.com/the-kalman-filter-for-financial-time-series/ describing the pros and cons of the Kalman Filters.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.