Pyramid Image Processing: Exploring the Depths of Visual Analysis

By Fouad Sabry

What is Pyramid Image Processing

Pyramid, or pyramid representation, is a type of multi-scale signal representation developed by the computer vision, image processing and signal processing communities, in which a signal or an image is subject to repeated smoothing and subsampling. Pyramid representation is a predecessor to scale-space representation and multiresolution analysis.

How you will benefit

(I) Insights, and validations about the following topics:

Chapter 1: Pyramid (image processing)

Chapter 2: Scale-invariant feature transform

Chapter 3: Gabor filter

Chapter 4: Scale space

Chapter 5: Gaussian blur

Chapter 6: Feature (computer vision)

Chapter 7: Difference of Gaussians

Chapter 8: Corner detection

Chapter 9: Structure tensor

Chapter 10: Mean shift

(II) Answering the public top questions about pyramid image processing.

(III) Real world examples for the usage of pyramid image processing in many fields.

Who this book is for

Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Pyramid Image Processing.

• Language: English
• Publisher: One Billion Knowledgeable
• Release date: May 11, 2024

Book preview

Chapter 1: Pyramid (image processing)

The pyramid representation, or pyramid for short, is a sort of multi-scale signal representation pioneered by researchers in the fields of computer vision, image processing, and signal processing. Before scale-space representation and multiresolution analysis, there was the pyramid representation.

Pyramids can be broken down into two broad categories: lowpass and bandpass.

After applying the necessary smoothing filter to the image, a lowpass pyramid is created by subsampling the result by a factor of 2 in both the horizontal and vertical directions. The resulting picture is processed in the same way once again, and this cycle is repeated several times. After several iterations, the image size decreases, the smoothness improves, but the spatial sampling density decreases (that is, decreased image resolution). Visually, the overall multi-scale representation resembles a pyramid, with the original image at the base and the smaller images produced by successive cycles layered atop it.

To enable the computation of pixel-wise differences, a bandpass pyramid is constructed by creating the difference between images at consecutive levels in the pyramid and conducting image interpolation between adjacent levels of resolution.

For pyramid generation, many smoothing kernels have been proposed. Today's more powerful processors make it possible to employ larger supported Gaussian filters as smoothing kernels in the pyramid creation processes.

Subsequent photos in a Gaussian pyramid are scaled down and weighted using a Gaussian average (Gaussian blur). Each neighborhood pixel in the lower levels of the pyramid is represented by a pixel with a local average. This method is widely employed in the field of texture synthesis.

Similar to a Gaussian pyramid, a Laplacian pyramid also stores the difference image between each degree of blurring. In order to reconstruct the high resolution image from the difference photos on higher levels, only the lowest level is not a difference image. Images can be compressed using this method.

Simoncelli and others invented the steerable pyramid, which is a multi-scale, multi-orientation band-pass filter bank used in image compression, texture generation, and object detection. It is similar to a Laplacian pyramid, but instead of using a single Laplacian or Gaussian filter at each level, a bank of steerable filters is employed.

Pyramids were the primary multi-scale representation utilized in early computer vision for generating multi-scale image attributes from raw image data. Some researchers favor scale-space representation because of its theoretical grounding, ability to decouple the subsampling stage from the multi-scale representation, more robust tools for theoretical analysis, and the ability to compute a representation at any desired scale, thereby avoiding the algorithmic problems of relating image representations at different resolutions. Pyramids aren't as popular as they once were, but they're nevertheless widely employed to convey computationally efficient approximations to scale-space representation.

Laplacian pyramids allow for the amplification or reduction of detail at various scales by adding or removing levels from the source image. However, it is well-known that this type of detail manipulation often results in halo errors, prompting the creation of alternatives like the bilateral filter.

The Adam7 algorithm, along with other interlacing techniques, is used in certain picture compression file formats. These can be seen as a pyramid shape for visuals. One file can support many viewer resolutions, rather than having to store or generate a different file for each resolution, thanks to the way those file formats store the large-scale features first and the fine-grain details later in the file. This allows a specific viewer displaying a small thumbnail or on a small screen to quickly download just enough of the image to display it in the available pixels.

{End Chapter 1}

Chapter 2: Scale-invariant feature transform

David Lowe developed the scale-invariant feature transform (SIFT) in 1999 as a computer vision algorithm for locating, characterizing, and matching local features in images. Object recognition, robotic mapping and navigation, image stitching, three-dimensional modeling, gesture recognition, video tracking, individual wildlife identification, and matchmaking are just some of the many possible uses for this technology.

Object SIFT keypoints are first extracted from a training set of images.

It is possible to create a feature description of any object in an image by isolating key points about that object. When trying to locate an object in a test image with many other objects, this description can be used because it was extracted from a training image. The features extracted from the training image must be discernible despite variations in image scale, noise, and illumination if reliable recognition is to be achieved. These spots typically reside on image edges or other areas with high contrast.

Furthermore, these features should maintain the same relative positions from one image to the next, as they did in the original scene. If only the four corners of a door were used as features, recognition would succeed whether the door was open or closed. However, if points in the frame were also used, recognition would fail in either case. Similarly, if there is any change in the internal geometry of an articulated or flexible object between two images in the set being processed, then the features located in that object will likely no longer function. While these local variations can have a significant impact on the average error of all feature matching errors, SIFT, in practice, detects and uses a much larger number of features from the images, which mitigates their impact.

This section provides a brief overview of the original SIFT algorithm and briefly discusses some alternative methods for object recognition in environments with a lot of background noise or obscured views.

The SIFT descriptor uses receptive-field measurements to analyze images.

Local image features can aid in object recognition if they can be detected and described. The SIFT features are not affected by resizing or rotating the image because they are based on the object's appearance at discrete interest points. They can withstand minor shifts in viewpoint as well as variations in illumination and noise. They also permit accurate object identification with a small chance of a mismatch, and they are highly unique and easy to extract. However, the high dimensionality can be a problem, so probabilistic algorithms like k-d trees with best bin first search are typically used. They are simple to match against a (large) database of local features. As few as three SIFT features from an object are needed to compute its location and pose, making object descriptions based on sets of SIFT features robust to partial occlusion. For relatively small databases and with today's computing power, recognition can be done almost instantly.

With Lowe's approach, an image is converted into a large set of feature vectors that are robust to local geometric distortion while still being invariant to image translation, scaling, and rotation and, to a lesser extent, changes in illumination. The neurons in the primary visual cortex, which encode basic form, color, and motion for object detection in primate vision, have similar properties to these features. Maximums and minimums of the difference of Gaussians function applied in scale space to a set