Joviša Žunić

Multigrid Convergence of Calculated Features in Image Analysis

This paper informs about number-theoretical and geometrical estimates of worst-case bounds for quantization errors in calculating features such as moments, moment based features, or perimeters in image analysis, and about probability-theoretical estimates of error bounds (e.g. standard deviations) for such digital approximations. New estimates (with proofs) and a review of previously known results are provided.

Measuring Elongation from Shape Boundary

Abstract Shape elongation is one of the basic shape descriptors that has a very clear intuitive meaning. That is the reason for its applicability in many shape classification tasks. In this paper we define a new method for computing shape elongation. The new measure is boundary based and uses all the boundary points. We start with shapes having polygonal boundaries. After that we extend the method to shapes with arbitrary boundaries. The new elongation measure converges when the assigned polygonal approximation converges toward a shape. We express the measure with closed formulas in both cases: for polygonal shapes and for arbitrary shapes. The new measure finds the elongation for shapes whose boundary is not extracted completely, which is impossible to achieve with area based measures.

On the maximal number of edges of convex digital polygons included into an m × m -grid

Abstract Let e(m) denote the maximal number of edges of a convex digital polygon included into an m × m square area of lattice points and let s(n) denote the minimal (side) size of a square in which a convex digital polygon with n edges can be included. We prove that e(m) = 12 (4π 2 ) 1 3 m 2 3 +O(m 1 3 log m) s(n) = 2τ 12 3 2 n 3 2 +O(n log n).

A new characterization of digital lines by least square fits

Abstract In this paper we prove that digital line segments and their least square line fits are in one-to-one correspondence and give a new simple representation ( x 1 , n , b 0 , b 1 ) of a digital line segment, where x 1 and n are the x -coordinate of the left endpoint and the number of digital points, respectively, while b 0 and b 1 are the coefficients of the least square line fit Y = b 0 + b 1 X for the given digital line segment. An O( n log n ) time algorithm for obtaining a digital line segment from its least square line fit is described.

A parametrization of digital planes by least-squares fits and generalizations

In this paper we prove that digital plane segments and their least-squares plane fit are in one-to-one correspondence, which gives a simple representation of a digital plane segment by its base description and coefficients of the least-squares plane fit. This leads to a constant space representation of digital rectangles in space. The method used is generalized and modified for constant space representation of sets which may consists of digital surface segments of different kinds.

On the number of linear partitions of the ( m,n -grid

Abstract A relationship between linear partitions and minimal pairs of a finite point set in the plane was established in [2]. This relationship is used here for counting the number of linear partitions of the set of points of the ( m, n )-grid, a rectangular part of the infinite grid. In order to optimize this counting, an O( mn ) algorithm is introduced for traversing all those pairs ( i, j ) of mutually simple natural numbers i and j , such that 1 ⩽ i ⩽ m , 1⩽ j ⩽ n .

Measuring shape ellipticity

A new ellipticity measure is proposed in this paper. The acquired shape descriptor shows how much the shape considered differs from a perfect ellipse. It is invariant to scale, translation, rotation and it is robust to noise and distortions. The new ellipticity measure ranges over (0, 1] and gives 1 if and only if the measured shape is an ellipse. The proposed measure is theoretically well founded, implying that the behaviour of the new measure can be well understand and predicted to some extent, what is always an advantage when select the set of descriptors for a certain application. Several experiments are provided to illustrate the behaviour and performance of the new measure.

Measuring Shape Circularity

In this paper we define a new circularity measure. The new measure is easy to compute and, being area based, is robust with respect to noise. It ranges over (0,1] and gives the measured circularity equal to 1 if and only if the measured shape is a circle. The new measure is invariant with respect to translations, rotations and scaling.

A Family of Shape Ellipticity Measures for Galaxy Classification

A new family of shape ellipticity measures is introduced. Each measure from the family distinguishes among the ellipses with different axis length ratios. This is not case for existing ellipticity measures. The new measures are theoretically well founded, which helps us to better understand their behavior and suitability to certain applications. All measures from the family are invariant with respect to translation, rotation, and scaling transformations; range over

Shape orientability

(0,1]