This confirms that the diploma thesis entitled "Face detection and recognition using skin segmentation and elastic graph matching" was submitted by Mr. Face detection' is the process of finding and extracting facial features in images or videos.
The Development of Face Recognition
General Concepts and Approaches
Popular Algorithms
- PCA or Principal Components Analysis
- LDA or Linear Discriminant Analysis
- SVM or Support Vector Machine
- EBGM or Elastic Bunch Graph Matching
- Trace Transform (Petrou & Kadyrov)
Recognition is based on the similarity of the Gabor filter response in each Gabor node. It consists of tracing the image with straight lines, along which certain values of the image function are calculated.
The digital image and its neighbourhood operations
Operations
Local operations - in which the output value of a pixel depends on the neighborhood defined around the coordinates of that pixel. Global operations - in which the output value of a particular point depends on all values in the input image.
Connectivity and CCA
Image Enhancement Tool: Contrast Stretching
In adaptive enhancement of an image, a window is convolved with the image and the local variance of the window is checked against the global variance (or a fraction of it) and the values are adjusted accordingly. The contrast stretch function used is a simple piecewise linear function, although sigmoid functions can also be used.
Mathematical Tools
- Convolution
- Mathematical Morphology (Gonzalez & Woods)
- Dilation
- Erosion
- Opening
- Hole filling
- Image Transforms: Gabor Filter and Gabor Transform
- Euler number (Saveliev)
As can be seen, the 'opening' process has resulted in the separation of object A into two components which were previously connected in the middle by a narrow isthmus. It determines the 'frequency' and 'phase' component of local sections of a signal as it changes over time.
The HSV Colour Space
Saturation: Represents the degree of color intensity of the color represented by the hue value. Value: It represents the intensity/luma of the color point and is therefore independent of the color intensity of the point.
Skin Segmentation
This data was used to define appropriate thresholds for the 'H' and 'S' space corresponding to faces. Skin segmentation is then performed by checking whether the 'H' and 'S' values of an input image in HSV space fall within the period indicated by the variance found in the corresponding histogram.
Removal of unwanted regions and noise
Morphological Cleaning
A morphological opening is then performed to remove very small objects from the image, while preserving the shape and size of larger objects. Morphological opening is again performed to remove small to medium areas that can be safely neglected as non-facial areas.
Connected Regions Analysis
- Rejections based on Geometry
- Euler Characteristic based Rejection
First, the mean and standard deviation of the region's intensity level are calculated. Otherwise, the threshold is set to a multiple of the standard deviation to ensure bright faces are taken into account.
Template Matching
In each run, the region with the highest match was blacked out to make it easier to find the region with the second highest match, and so on. The results of the template matching algorithm are the coordinates of the faces where the size of the area is the same as the average image.
Results of the Detection Process
Ideally, the cropped images of faces extracted by the face detector should be fed into the identifier. However, since a proper database of faces under controlled conditions could not be built, the developed algorithm was tested on existing databases obtained from the Internet.
Elastic Bunch Graph Matching or EBGM
Correlation between image and graph
Every two nodes in the graph are connected by an edge, which is represented by the size of the length of the edge. These constitute a basic structure of the face graph that is sufficient to distinguish between other non-face graphs that will have a different structure.
Preprocessing (Gabor Wavelets)
- Comparison between Jets
- Calculation of Displacement, d
- Face graph Representation
To calculate the offset factor, the phase-sensitive similarity function is extended. The basic idea is to maximize the phase-dependent similarity function and calculate the compensation required by the shift factor.
Face Bunch Graphing
That is, for each person, a set of face segments is used as a model image set and a face cluster graph is generated that uniquely represents the facial features of that person. This face group graph has a set of rays extracted from each model image that represents a particular person.
Elastic Bunch Graph Matching
- Manual generation of graph
- Matching using Graph Similarity Function
The Elastic Bunch Graph Matching is responsible for the similarity between the input image graph and the face bundle g-position. This process is Elastic Bunch Graph Match pixel location of the confidence points in the face bunch g.
Face Recognition based on Similarity Measure
Now if the recognition index is 0, then the picture does not match the database and is not recognized. If the recognition index is the same with every single weight (W1, W2,…W5), then it is perfect recognition and the image is recognized as one of the 5 people.
Result analysis for Facial Recognition
After the face cluster graph is generated for each of the 5 aforementioned persons, they are trained with image graphs that are of the same persons to find a lower bound for the threshold value of the similarity measure below which the image graph should be considered as not matching the face cluster graph. Therefore, when an arbitrary image graph is given as input to the recognizer, a similarity measure is calculated with all the 5 Face Bunch Graphs individually, and if they match their individual threshold criteria, they are considered a match for.
Matching Accuracy
So the generated 'recognition index' has a unique weight that successfully recognizes the person on the input image graph.
Limitations
Databases Used
Convolution of two functions a and b
Thus, the comparison between images aims to assess the similarity in the structure of the facial segments. From this it can be deduced that a facial feature causes a small variation in the strength of the rays, regardless of the degree of brightness and contrast variation. Including the displacement factor can also iteratively point to the radius that will maximize neighborhood similarity.
This process is Elastic Bunch Graph Matching, because according to the reference points in the facebos graph, the neighborhood of the same pixel in the image graph is elastically expanded to find a set of reference nodes for which the similarity between the two points is maximum. the i.
Convolution in discrete 2D space
Dilation
This structuring element, B, is first modified by obtaining its reflection about its origin and translating this reflection by z.
Erosion
In words, this equation means that the erosion gives all translations in which B translated with z is contained. Opening is usually used to break the tight connections between two bounding blocks to get separate bonding.
Opening
As can be observed, the 'opening' process led to the separation of o two components, which were earlier connected in the middle by a As can be observed, the 'opening' process led to the separation of o two components , which used to be connected in the middle by a. Denote by A, a set whose elements are a boundary that encloses a background region (or inside each hole, the goal is to fill all the holes.
Hole filling
A 'hole' can be defined as a background area surrounded by a connected border of foreground pixels. The process begins by making a set of zeros, X0, which is from the same beam containing A, except at the locations in X0 that correspond to the sample point in each hole, which is set to the value with which the hole is to be filled (255 for binary image).
Gabor Filter in 2D
Rotated parameters in Gabor filter
The Gabor transform
Then, the 'Euler number', or 'Euler characteristic', of the image is stated as the 'alternative sum of the number of cells of each dimension'.
Finding out the Euler number
Therefore, the projection of the point onto the base 2-D plane represents only the chroma component of the color and the luma component is separated and ignored. The HSV color space sizes can be generated for a color point if the RGB color space size is known, using the following transformations:.
Conversion to HSV from RGB
If there is a large spread and the ratio of mean to standard deviation is high, the threshold is set to a fraction of the mean. In turn, the nodes are identified by wavelet responses from local rays, and the edges are identified by the length of the edge.
Convolution with Gabor Kernels to generate wavelet transformed image
Family of Gabor Kernels for j varying from 0 to 39
Wave vector kj for j varying from 1 to 39
Robustness is also defined because the result of the transformation is not sensitive to variation in brightness when the Gabor wavelets are considered DC-free. So if we ignore the phase of the jets, the jet size remains similar for the nearby pixels representing the same local feature.
Similarity measure
The inclusion of phase dependence is therefore important to make the similarity function more robust to pattern variations in a more accurate manner. For the compensation factor, it is assumed that the rays compared in the similarity function belong to the nearby point and therefore have a small displacement between them.
Similarity Function S for jets including phase
Taylor Series expansion of phase included similarity function
Displacement Vector
These sets of nodes are stacked and the set of edges between similar reference points are averaged to generate the face base graph corresponding to a particular person. In our analysis, we selected for representative purposes a set of 5 individuals, and therefore 5 face-bottom graphs are generated, one for each of them.
Graph Similarity Measure between image graph and bunch graph
After generating the model forest graph for the representative set of faces, the goal is to match each individual bundle graph to an input image graph and grade it using a similarity function that measures the degree of similarity or distortion between the face structures represented by the graphs. . Therefore, taking the nodal location of the rays in the face group graph and base and considering the location constraints, the similarity estimation is done for 25 pixel point per node for the image graph, and the pixel point set where the similarity is maximum is taken as the measure of similarity between the image graph and that particular face group graph.
Recognition Index for the database used for analysis
For the face recognition system, the Elastic Bunch Graph Matching algorithm is designed and implemented on a test database of about 30 facial image segments. The designed algorithm is robust to distortions in expressions and pose variations and hence can easily train the Face Set Graph representing an individual with a set of 4-5 training images.
