Intelligent Vision Systems ENT 496 Object Shape Identification and Representation Hema C.R. Lecture 7

Hema ENT 496 Lecture 7 2 Road Map Contour Chain codes Object Recognition Object Representation Feature Detection Hough Transform Fourier Descriptors

Hema ENT 496 Lecture 7 3 Contour Represented as ordered list of edges or a curve Criteria for good contour –Efficiency: simple and compact representation –Accuracy: accurately fit image features –Effectiveness: suitable for operations to be performed at a later stage

Hema ENT 496 Lecture 7 4 Definitions Edge list –Ordered set of edge points or fragments Contour –Edge list or a curve that is used to represent the edge list Boundary –Closed contour that surrounds a region Note: The term edge generally refers to edge points

Hema ENT 496 Lecture 7 5 Chain Codes Notation for recording list of edge points along contour Chain code specifies the direction of the contour at each edge Directions are quantized into one of eight directions These codes are also known as freeman codes Are used for the description of pixel border Local information of the objects can be obtained from the chain code –E.g. where image border turns 90 degrees etc.

Hema ENT 496 Lecture Chain coding example

Hema ENT 496 Lecture 7 7 Object Recognition Object recognition systems find objects in the real world from an image of the world. Object recognition can be defined as a labeling problem based on models of known objects.

Hema ENT 496 Lecture 7 8 Components of a object recognition system Model database – model base Feature detector Hypothesizer Hypothesis verifier Feature Detector Hypothesis Formation Hypothesis verification Modelbase Image Features Candidate objects Object Class

Hema ENT 496 Lecture 7 9 Components Model Database –Contains all models known to the system for recognition –such as size, color, shape, CAD drawing etc Feature Detector –Applies operators to images and identifies location of features that help the object hypothesis Hypothesizer –Assigns likelihood to objects using features detected and selects object with highest likelihood Hypothesis Verifier –Uses object models to select most likely object Note: Depending on the complexity of the problems one or more modules becomes trivial.

Hema ENT 496 Lecture 7 10 Object Representation Observer-Centered Representation –Applied to objects relatively in stable positions w.r. to camera –Global features of a scene are recognized –Features are selected based on experience of designer or analyzing features to form object groups Object-Centered Representation –Uses description of objects based on usually 3D –Independent of camera parameters –Used in constructive solid geometry e.g. CAD / CAM

Hema ENT 496 Lecture 7 11 Feature Detection Global Features –Characteristic of a region Area Perimeter Fourier Descriptors Moments Local Features –Features on the boundary of an object or a small region Curvature Boundary segment Corners Relational Features –Based on relative positions of different entities like regions, closed contours etc. Distance between features Used in defining composite objects

Hema ENT 496 Lecture 7 12 Recognition Strategies Object recognition is a sequence of steps that is performed after appropriate features have been detected. Not all object recognition techniques require strong hypothesis formation and verification steps Hypothesizer Classifier Verifier Sequential Matching HypothesizerVerifier FeaturesObject Features Object

Hema ENT 496 Lecture 7 13 Strategies Classification –Nearest neighbor Similar features in a region are clustered, based on a centroid and distance –Bayesian Classifier Used when distribution of objects is not straightforward When there is an overlap of features of different objects. Probabilistic knowledge about features and frequency of objects is used –Neural Nets Implement a classification approach Use nonlinear boundary partition of features Boundaries are used by training a net –Off-line computations Computations are done before recognition Recognition process can be converted to a look-up table Matching –Feature Matching Known features of the object are matched with unknown objects feature to find matches –Symbolic Matching Relation among features are matched Graph matching

Hema ENT 496 Lecture 7 14 Hough Transform The Hough transform is a feature extraction technique The classical transform identifies lines in the image, but it has been extended to identifying positions of arbitrary shapes. The transform universally used today was invented by Richard Duda and Peter Hart in 1972, who called it a "generalized Hough transform" after the related 1962 patent of Paul Hough.

Hema ENT 496 Lecture 7 15 Hough Transform- Theory The underlying principle –there are an infinite number of potential lines that pass through any point, each at a different orientation. The purpose of the transform is to determine which of these theoretical lines pass through most features in an image –that is, which lines fit most closely to the data in the image. In order to determine that two points lie on the same potential line, it is necessary to create a representation of a line that allows meaningful comparison. In the standard Hough transform, each line is represented by two parameters, commonly called r and θ (theta) –which represent the length and angle from the origin of a normal to the line in question

Hema ENT 496 Lecture 7 16 Hough Transform- Theory By transforming all the possible lines through a point into this coordinate system – i.e. calculating the value of r for every possible value of θ - a sinusoidal curve is created which is unique to that point. This representation of the two parameters is sometimes referred to as Hough space. If the curves corresponding to two points are superimposed, the location (in Hough space) where they cross correspond to lines (in the original image space) which pass through both points. A set of points which form a straight line will produce Hough transforms which cross at the parameters for that line.

Hema ENT 496 Lecture 7 17 Hough Transform for three data points Procedure to create a Hough space graph For each data point  A number of lines are plotted going through it, all at different angles. These are shown as solid lines.  For each solid line a line is plotted which is perpendicular to it and which intersects the origin. These are shown as dashed lines.  The length and angle of each dashed line is measured. The results are shown in tables.  This is repeated for each data point.  A graph of length against angle, known as a Hough space graph, is then created Hough Space Graph

Hema ENT 496 Lecture 7 18 Fourier Descriptors Fourier descriptors are compact representation for closed contours Boundary of an object can be expressed as a sequence of co-ordinates Each co-ordinate pair can be represented as a complex number such that X axis is treated as the real axis and y axis is treated as the imaginary axis of a series of complex numbers This sequence is periodic with period N and boundary is represented in one dimension (1)

Hema ENT 496 Lecture 7 19 Discrete Fourier Transform DFT of a one dimensional sequence u(n) is defined as The Complex coefficients a(k) are called the Fourier descriptors of the boundary (3) (2)

Hema ENT 496 Lecture 7 20 Covariance Covariance of two features gives a relation between the two features The covariance is computed as Where n is number of patterns [facial] and and are the mean of features of X and Y respectively –If covariance value is positive then if X increases Y also increases –If covariance value is negative when X increases and Y decrease –If covariance is zero there is no relation between X and Y features (4)

Intelligent Vision Systems Object Shape Identification and Representation Hema C.R. Object Shape Identification and Representation Hema C.R. End of Lecture 7