2 research outputs found
Primena novih deskriptora oblika i teorije neodreΔenosti u obradi slike
The doctoral thesis deals with the study of quantitative aspects of shape attribute ssuitable for numerical characterization, i.e., shape descriptors, as well as the theory of uncertainty, particularly the theory of fuzzy sets, and their application in image processing. The original contributions and results of the thesis can be naturally divided into two groups, in accordance with the approaches used to obtain them. The first group of contributions relates to introducing new shape descriptors (of hexagonality and fuzzy squareness) and associated measures that evaluate to what extent the shape considered satisfies these properties. The introduced measures are naturally defined, theoretically well-founded, and satisfy most of the desirable properties expected to be satisfied by each well-defined shape measure. To mention some of them: they both range through (0,1] and achieve the largest possible value 1 if and only if the shape considered is a hexagon, respectively a fuzzy square; there is no non-zero area shape with the measured hexagonality or fuzzy squareness equal to 0; both introduced measures are invariant to similarity transformations; and provide results that are consistent with the theoretically proven results, as well as human perception and expectation. Numerous experiments on synthetic and real examples are shown aimed to illustrate theoretically proven considerations and to provide clearer insight into the behaviour of the introduced shape measures. Their advantages and applicability are illustrated in various tasks of recognizing and classifying objects images of several well-known and most frequently used image datasets. Besides, the doctoral thesis contains research related to the application of the theory of uncertainty, in the narrower sense fuzzy set theory, in the different tasks of image processing and shape analysis. We distinguish between the tasks relating to the extraction of shape features, and those relating to performance improvement of different image processing and image analysis techniques. Regarding the first group of tasks, we deal with the application of fuzzy set theory in the tasks of introducing new fuzzy shape-based descriptor, named fuzzy squareness, and measuring how much fuzzy square is given fuzzy shape. In the second group of tasks, we deal with the study of improving the performance of estimates of both the Euclidean distance transform in three dimensions (3D EDT) and the centroid distance signature of shape in two dimensions. Performance improvement is particularly reflected in terms of achieved accuracy and precision, increased invariance to geometrical transformations (e.g., rotation and translation), and robustness in the presence of noise and uncertainty resulting from the imperfection of devices or imaging conditions. The latter also refers to the second group of the original contributions and results of the thesis. It is motivated by the fact that the shape analysis traditionally assumes that the objects appearing in the image are previously uniquely and crisply extracted from the image. This is usually achieved in the process of sharp (i.e., binary) segmentation of the original image where a decision on the membership of point to an imaged object is made in a sharp manner. Nevertheless, due to the imperfections of imaging conditions or devices, the presence of noise, and various types of imprecision (e.g., lack of precise object boundary or clear boundaries between the objects, errors in computation, lack of information, etc.), different levels of uncertainty and vagueness in the process of making a decision regarding the membership of image point may potentially occur. This is particularly noticeable in the case of discretization (i.e., sampling) of continuous image domain when a single image element, related to corresponding image sample point, iscovered by multiple objects in an image. In this respect, it is clear that this type of segmentation can potentially lead to a wrong decision on the membership of image points, and consequently irreversible information loss about the imaged objects. This stems from the fact that image segmentation performed in this way does not permit that the image point may be a member to a particular imaged object to some degree, further leading to the potential risk that points partially contained in the object before segmentation will not be assigned to the object after segmentation. However, if instead of binary segmentation, it is performed segmentation where a decision about the membership of image point is made in a gradual rather than crisp manner, enabling that point may be a member to an object to some extent, then making a sharp decision on the membership can be avoided at this early analysis step. This further leads that potentially a large amount of object information can be preserved after segmentation and used in the following analysis steps. In this regard, we are interested in one specific type of fuzzy segmentation, named coverage image segmentation, resulting in fuzzy digital image representation where membership value assigned to each image element is proportional to its relative coverage by a continuous object present in the original image. In this thesis, we deal with the study of coverage digitization model providing coverage digital image representation and present how significant improvements in estimating 3D EDT, as well as the centroid distance signature of continuous shape, can be achieved, if the coverage information available in this type of image representation is appropriately considered.ΠΠΎΠΊΡΠΎΡΡΠΊΠ° Π΄ΠΈΡΠ΅ΡΡΠ°ΡΠΈΡΠ° ΡΠ΅ Π±Π°Π²ΠΈ ΠΏΡΠΎΡΡΠ°Π²Π°ΡΠ΅ΠΌ ΠΊΠ²Π°Π½ΡΠΈΡΠ°ΡΠΈΠ²Π½ΠΈΡ
Π°ΡΠΏΠ΅ΠΊΠ°ΡΠ° Π°ΡΡΠΈΠ±ΡΡΠ° ΠΎΠ±Π»ΠΈΠΊΠ° ΠΏΠΎΠ³ΠΎΠ΄Π½ΠΈΡ
Π·Π° Π½ΡΠΌΠ΅ΡΠΈΡΠΊΡ ΠΊΠ°ΡΠ°ΠΊΡΠ΅ΡΠΈΠ·Π°ΡΠΈΡΡ, ΡΠΎ ΡΠ΅ΡΡ Π΄Π΅ΡΠΊΡΠΈΠΏΡΠΎΡΠ° ΠΎΠ±Π»ΠΈΠΊΠ°, ΠΊΠ°ΠΎ ΠΈ ΡΠ΅ΠΎΡΠΈΡΠΎΠΌ Π½Π΅ΠΎΠ΄ΡΠ΅ΡΠ΅Π½ΠΎΡΡΠΈ, ΠΏΠΎΡΠ΅Π±Π½ΠΎ ΡΠ΅ΠΎΡΠΈΡΠΎΠΌ ΡΠ°Π·ΠΈ ΡΠΊΡΠΏΠΎΠ²Π°, ΠΈ ΡΠΈΡ
ΠΎΠ²ΠΎΠΌ ΠΏΡΠΈΠΌΠ΅Π½ΠΎΠΌ Ρ ΠΎΠ±ΡΠ°Π΄ΠΈ ΡΠ»ΠΈΠΊΠ΅. ΠΡΠΈΠ³ΠΈΠ½Π°Π»Π½ΠΈ Π΄ΠΎΠΏΡΠΈΠ½ΠΎΡΠΈ ΠΈ ΡΠ΅Π·ΡΠ»ΡΠ°ΡΠΈ ΡΠ΅Π·Π΅ ΠΌΠΎΠ³Ρ ΡΠ΅ ΠΏΡΠΈΡΠΎΠ΄Π½ΠΎ ΠΏΠΎΠ΄Π΅Π»ΠΈΡΠΈ Ρ Π΄Π²Π΅ Π³ΡΡΠΏΠ΅, Ρ ΡΠΊΠ»Π°Π΄Ρ ΡΠ° ΠΏΡΠΈΡΡΡΠΏΠΎΠΌ ΠΈ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ»ΠΎΠ³ΠΈΡΠΎΠΌ ΠΊΠΎΡΠ° ΡΠ΅ ΠΊΠΎΡΠΈΡΡΠ΅Π½Π° Π·Π° ΡΠΈΡ
ΠΎΠ²ΠΎ Π΄ΠΎΠ±ΠΈΡΠ°ΡΠ΅. ΠΡΠ²Π° Π³ΡΡΠΏΠ° Π΄ΠΎΠΏΡΠΈΠ½ΠΎΡΠ° ΠΎΠ΄Π½ΠΎΡΠΈ ΡΠ΅ Π½Π° ΡΠ²ΠΎΡΠ΅ΡΠ΅ Π½ΠΎΠ²ΠΈΡ
Π΄Π΅ΡΠΊΡΠΈΠΏΡΠΎΡΠ° ΠΎΠ±Π»ΠΈΠΊΠ° (ΡΠ΅ΡΡΠΎΡΠ³Π°ΠΎΠ½ΠΎΡΡΠΈ ΠΈ ΡΠ°Π·ΠΈ ΠΊΠ²Π°Π΄ΡΠ°ΡΠ½ΠΎΡΡΠΈ) ΠΊΠ°ΠΎ ΠΈ ΠΎΠ΄Π³ΠΎΠ²Π°ΡΠ°ΡΡΡΠΈΡ
ΠΌΠ΅ΡΠ° ΠΊΠΎΡΠ΅ Π½ΡΠΌΠ΅ΡΠΈΡΠΊΠΈ ΠΎΡΠ΅ΡΡΡΡ Ρ ΠΊΠΎΠΌ ΠΎΠ±ΠΈΠΌΡ ΡΠ°Π·ΠΌΠ°ΡΡΠ°Π½ΠΈ ΠΎΠ±Π»ΠΈΠΊ Π·Π°Π΄ΠΎΠ²ΠΎΡΠ°Π²Π° ΡΠ°Π·ΠΌΠ°ΡΡΠ°Π½Π° ΡΠ²ΠΎΡΡΡΠ²Π°. Π£Π²Π΅Π΄Π΅Π½Π΅ ΠΌΠ΅ΡΠ΅ ΡΡ ΠΏΡΠΈΡΠΎΠ΄Π½ΠΎ Π΄Π΅ΡΠΈΠ½ΠΈΡΠ°Π½Π΅, ΡΠ΅ΠΎΡΠΈΡΡΠΊΠΈ Π΄ΠΎΠ±ΡΠΎ Π·Π°ΡΠ½ΠΎΠ²Π°Π½Π΅ ΠΈ Π·Π°Π΄ΠΎΠ²ΠΎΡΠ°Π²Π°ΡΡ Π²Π΅ΡΠΈΠ½Ρ ΠΏΠΎΠΆΠ΅ΡΠ½ΠΈΡ
ΡΠ²ΠΎΡΡΡΠ°Π²Π° ΠΊΠΎΡΠ΅ ΡΠ²Π°ΠΊΠ° Π΄ΠΎΠ±ΡΠΎ Π΄Π΅ΡΠΈΠ½ΠΈΡΠ°Π½Π° ΠΌΠ΅ΡΠ° ΠΎΠ±Π»ΠΈΠΊΠ° ΡΡΠ΅Π±Π° Π΄Π° Π·Π°Π΄ΠΎΠ²ΠΎΡΠ°Π²Π°. ΠΠΎΠΌΠ΅Π½ΠΈΠΌΠΎ Π½Π΅ΠΊΠ΅ ΠΎΠ΄ ΡΠΈΡ
: ΠΎΠ±Π΅ ΠΌΠ΅ΡΠ΅ ΡΠ·ΠΈΠΌΠ°ΡΡ Π²ΡΠ΅Π΄Π½ΠΎΡΡΠΈ ΠΈΠ· ΠΈΠ½ΡΠ΅ΡΠ²Π°Π»Π° (0,1] ΠΈ Π΄ΠΎΡΡΠΈΠΆΡ Π½Π°ΡΠ²Π΅ΡΡ ΠΌΠΎΠ³ΡΡΡ Π²ΡΠ΅Π΄Π½ΠΎΡΡ 1 Π°ΠΊΠΎ ΠΈ ΡΠ°ΠΌΠΎ Π°ΠΊΠΎ ΡΠ΅ ΠΎΠ±Π»ΠΈΠΊ ΠΊΠΎΡΠΈ ΡΠ΅ ΠΏΠΎΡΠΌΠ°ΡΡΠ° ΡΠ΅ΡΡΠΎΡΠ³Π°ΠΎ, ΠΎΠ΄Π½ΠΎΡΠ½ΠΎ ΡΠ°Π·ΠΈ ΠΊΠ²Π°Π΄ΡΠ°Ρ; Π½Π΅ ΠΏΠΎΡΡΠΎΡΠΈ ΠΎΠ±Π»ΠΈΠΊ Π½Π΅-Π½ΡΠ»Π° ΠΏΠΎΠ²ΡΡΠΈΠ½Π΅ ΡΠΈΡΠ° ΡΠ΅ ΠΈΠ·ΠΌΠ΅ΡΠ΅Π½Π° ΡΠ΅ΡΡΠΎΡΠ³Π°ΠΎΠ½ΠΎΡΡ, ΠΎΠ΄Π½ΠΎΡΠ½ΠΎ ΡΠ°Π·ΠΈ ΠΊΠ²Π°Π΄ΡΠ°ΡΠ½ΠΎΡΡ ΡΠ΅Π΄Π½Π°ΠΊΠ° 0; ΠΎΠ±Π΅ ΡΠ²Π΅Π΄Π΅Π½Π΅ ΠΌΠ΅ΡΠ΅ ΡΡ ΠΈΠ½Π²Π°ΡΠΈΡΠ°Π½ΡΠ½Π΅ Ρ ΠΎΠ΄Π½ΠΎΡΡ Π½Π° ΡΡΠ°Π½ΡΡΠΎΡΠΌΠ°ΡΠΈΡΠ΅ ΡΠ»ΠΈΡΠ½ΠΎΡΡΠΈ; ΠΈ Π΄Π°ΡΡ ΡΠ΅Π·ΡΠ»ΡΠ°ΡΠ΅ ΠΊΠΎΡΠΈ ΡΡ Ρ ΡΠΊΠ»Π°Π΄Ρ ΡΠ° ΡΠ΅ΠΎΡΠΈΡΡΠΊΠΈ Π΄ΠΎΠΊΠ°Π·Π°Π½ΠΈΠΌ ΡΠ΅Π·ΡΠ»ΡΠ°ΡΠΈΠΌΠ°, ΠΊΠ°ΠΎ ΠΈ ΡΡΠ΄ΡΠΊΠΎΠΌ ΠΏΠ΅ΡΡΠ΅ΠΏΡΠΈΡΠΎΠΌ ΠΈ ΠΎΡΠ΅ΠΊΠΈΠ²Π°ΡΠΈΠΌΠ°. ΠΡΠΎΡΠ½ΠΈ Π΅ΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠΈ Π½Π° ΡΠΈΠ½ΡΠ΅ΡΠΈΡΠΊΠΈΠΌ ΠΈ ΡΠ΅Π°Π»Π½ΠΈΠΌ ΠΏΡΠΈΠΌΠ΅ΡΠΈΠΌΠ° ΠΏΡΠΈΠΊΠ°Π·Π°Π½ΠΈ ΡΡ Ρ ΡΠΈΡΡ ΠΈΠ»ΡΡΡΡΠΎΠ²Π°ΡΠ° ΡΠ΅ΠΎΡΠΈΡΡΠΊΠΈ Π΄ΠΎΠΊΠ°Π·Π°Π½ΠΈΡ
ΡΠ°Π·ΠΌΠ°ΡΡΠ°ΡΠ° ΠΈ ΠΏΡΡΠΆΠ°ΡΠ° ΡΠ°ΡΠ½ΠΈΡΠ΅Π³ ΡΠ²ΠΈΠ΄Π° Ρ ΠΏΠΎΠ½Π°ΡΠ°ΡΠ΅ ΡΠ²Π΅Π΄Π΅Π½ΠΈΡ
ΠΌΠ΅ΡΠ°. ΠΠΈΡ
ΠΎΠ²Π° ΠΏΡΠ΅Π΄Π½ΠΎΡΡ ΠΈ ΠΊΠΎΡΠΈΡΠ½ΠΎΡΡ ΠΈΠ»ΡΡΡΡΠΎΠ²Π°Π½ΠΈ ΡΡ Ρ ΡΠ°Π·Π»ΠΈΡΠΈΡΠΈΠΌ Π·Π°Π΄Π°ΡΠΈΠΌΠ° ΠΏΡΠ΅ΠΏΠΎΠ·Π½Π°Π²Π°ΡΠ° ΠΈ ΠΊΠ»Π°ΡΠΈΡΠΈΠΊΠ°ΡΠΈΡΠ΅ ΡΠ»ΠΈΠΊΠ° ΠΎΠ±ΡΠ΅ΠΊΠ°ΡΠ° Π½Π΅ΠΊΠΎΠ»ΠΈΠΊΠΎ ΠΏΠΎΠ·Π½Π°ΡΠΈΡ
ΠΈ Π½Π°ΡΡΠ΅ΡΡΠ΅ ΠΊΠΎΡΠΈΡΡΠ΅Π½ΠΈΡ
Π±Π°Π·Π° ΡΠ»ΠΈΠΊΠ°. ΠΠΎΡΠ΅Π΄ ΡΠΎΠ³Π°, Π΄ΠΎΠΊΡΠΎΡΡΠΊΠ° ΡΠ΅Π·Π° ΡΠ°Π΄ΡΠΆΠΈ ΠΈΡΡΡΠ°ΠΆΠΈΠ²Π°ΡΠ° Π²Π΅Π·Π°Π½Π° Π·Π° ΠΏΡΠΈΠΌΠ΅Π½Ρ ΡΠ΅ΠΎΡΠΈΡΠ΅ Π½Π΅ΠΎΠ΄ΡΠ΅ΡΠ΅Π½ΠΎΡΡΠΈ, Ρ ΡΠΆΠ΅ΠΌ ΡΠΌΠΈΡΠ»Ρ ΡΠ΅ΠΎΡΠΈΡΠ΅ ΡΠ°Π·ΠΈ ΡΠΊΡΠΏΠΎΠ²Π°, Ρ ΡΠ°Π·Π»ΠΈΡΠΈΡΠΈΠΌ Π·Π°Π΄Π°ΡΠΈΠΌΠ° ΠΎΠ±ΡΠ°Π΄Π΅ ΡΠ»ΠΈΠΊΠ΅ ΠΈ Π°Π½Π°Π»ΠΈΠ·Π΅ ΠΎΠ±Π»ΠΈΠΊΠ°. Π Π°Π·Π»ΠΈΠΊΡΡΠ΅ΠΌΠΎ Π·Π°Π΄Π°ΡΠΊΠ΅ ΠΊΠΎΡΠΈ ΡΠ΅ ΠΎΠ΄Π½ΠΎΡΠ΅ Π½Π° ΠΈΠ·Π΄Π²Π°ΡΠ°ΡΠ΅ ΠΊΠ°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠ° ΠΎΠ±Π»ΠΈΠΊΠ° ΠΈ ΠΎΠ½Π΅ ΠΊΠΎΡΠΈ ΡΠ΅ ΠΎΠ΄Π½ΠΎΡΠ΅ Π½Π° ΠΏΠΎΠ±ΠΎΡΡΠ°ΡΠ΅ ΠΏΠ΅ΡΡΠΎΡΠΌΠ°Π½ΡΠΈ ΡΠ°Π·Π»ΠΈΡΠΈΡΠΈΡ
ΡΠ΅Ρ
Π½ΠΈΠΊΠ° ΠΎΠ±ΡΠ°Π΄Π΅ ΠΈ Π°Π½Π°Π»ΠΈΠ·Π΅ ΡΠ»ΠΈΠΊΠ΅. Π¨ΡΠΎ ΡΠ΅ ΡΠΈΡΠ΅ ΠΏΡΠ²Π΅ Π³ΡΡΠΏΠ΅ Π·Π°Π΄Π°ΡΠ°ΠΊΠ°, Π±Π°Π²ΠΈΠΌΠΎ ΡΠ΅ ΠΏΡΠΈΠΌΠ΅Π½ΠΎΠΌ ΡΠ΅ΠΎΡΠΈΡΠ΅ ΡΠ°Π·ΠΈ ΡΠΊΡΠΏΠΎΠ²Π° Ρ Π·Π°Π΄Π°ΡΠΈΠΌΠ° Π΄Π΅ΡΠΈΠ½ΠΈΡΠ°ΡΠ° Π½ΠΎΠ²ΠΎΠ³ Π΄Π΅ΡΠΊΡΠΈΠΏΡΠΎΡΠ° ΡΠ°Π·ΠΈ ΠΎΠ±Π»ΠΈΠΊΠ°, Π½Π°Π·Π²Π°Π½ ΡΠ°Π·ΠΈ ΠΊΠ²Π°Π΄ΡΠ°ΡΠ½ΠΎΡΡ, ΠΈ ΠΌΠ΅ΡΠ΅ΡΠ° ΠΊΠΎΠ»ΠΈΠΊΠΎ ΡΠ΅ ΡΠ°Π·ΠΈ ΠΊΠ²Π°Π΄ΡΠ°ΡΠ°Π½ ΠΏΠΎΡΠΌΠ°ΡΡΠ°Π½ΠΈ ΡΠ°Π·ΠΈ ΠΎΠ±Π»ΠΈΠΊ. Π£ Π΄ΡΡΠ³ΠΎΡ Π³ΡΡΠΏΠΈ Π·Π°Π΄Π°ΡΠ°ΠΊΠ° Π±Π°Π²ΠΈΠΌΠΎ ΡΠ΅ ΠΈΡΡΡΠ°ΠΆΠΈΠ²Π°ΡΠ΅ΠΌ ΠΏΠΎΠ±ΠΎΡΡΠ°ΡΠ° ΠΏΠ΅ΡΡΠΎΡΠΌΠ°Π½ΡΠΈ ΠΎΡΠ΅Π½Π΅ ΡΡΠ°Π½ΡΡΠΎΡΠΌΠ°ΡΠΈΡΠ΅ ΡΠ»ΠΈΠΊΠ΅ Π΅ΡΠΊΠ»ΠΈΠ΄ΡΠΊΠΈΠΌ ΡΠ°ΡΡΠΎΡΠ°ΡΠΈΠΌΠ° Ρ ΡΡΠΈ Π΄ΠΈΠΌΠ΅Π½Π·ΠΈΡΠ΅ (3Π ΠΠΠ’), ΠΊΠ°ΠΎ ΠΈ ΡΠΈΠ³Π½Π°ΡΡΡΠ΅ Π½Π΅ΠΏΡΠ΅ΠΊΠΈΠ΄Π½ΠΎΠ³ ΠΎΠ±Π»ΠΈΠΊΠ° Ρ Π΄Π²Π΅ Π΄ΠΈΠΌΠ΅Π½Π·ΠΈΡΠ΅ Π·Π°ΡΠ½ΠΎΠ²Π°Π½Π΅ Π½Π° ΡΠ°ΡΡΠΎΡΠ°ΡΡ ΠΎΠ΄ ΡΠ΅Π½ΡΡΠΎΠΈΠ΄Π° ΠΎΠ±Π»ΠΈΠΊΠ°. ΠΠ²ΠΎ ΠΏΠΎΡΠ»Π΅Π΄ΡΠ΅ ΡΠ΅ ΠΏΠΎΡΠ΅Π±Π½ΠΎ ΠΎΠ³Π»Π΅Π΄Π° Ρ ΠΏΠΎΡΡΠΈΠ³Π½ΡΡΠΎΡ ΡΠ°ΡΠ½ΠΎΡΡΠΈ ΠΈ ΠΏΡΠ΅ΡΠΈΠ·Π½ΠΎΡΡΠΈ ΠΎΡΠ΅Π½Π΅, ΠΏΠΎΠ²Π΅ΡΠ°Π½ΠΎΡ ΠΈΠ½Π²Π°ΡΠΈΡΠ°Π½ΡΠ½ΠΎΡΡΠΈ Ρ ΠΎΠ΄Π½ΠΎΡΡ Π½Π° ΡΠΎΡΠ°ΡΠΈΡΡ ΠΈ ΡΡΠ°Π½ΡΠ»Π°ΡΠΈΡΡ ΠΎΠ±ΡΠ΅ΠΊΡΠ°, ΠΊΠ°ΠΎ ΠΈ ΡΠΎΠ±ΡΡΡΠ½ΠΎΡΡΠΈ Ρ ΠΏΡΠΈΡΡΡΡΠ²Ρ ΡΡΠΌΠ° ΠΈ Π½Π΅ΠΎΠ΄ΡΠ΅ΡΠ΅Π½ΠΎΡΡΠΈ ΠΊΠΎΡΠ΅ ΡΡ ΠΏΠΎΡΠ»Π΅Π΄ΠΈΡΠ° Π½Π΅ΡΠ°Π²ΡΡΠ΅Π½ΠΎΡΡΠΈ ΡΡΠ΅ΡΠ°ΡΠ° ΠΈΠ»ΠΈ ΡΡΠ»ΠΎΠ²Π° ΡΠ½ΠΈΠΌΠ°ΡΠ°. ΠΠΎΡΠ»Π΅Π΄ΡΠΈ ΡΠ΅Π·ΡΠ»ΡΠ°ΡΠΈ ΡΠ΅ ΡΠ°ΠΊΠΎΡΠ΅ ΠΎΠ΄Π½ΠΎΡΠ΅ ΠΈ Π½Π° Π΄ΡΡΠ³Ρ Π³ΡΡΠΏΡ ΠΎΡΠΈΠ³ΠΈΠ½Π°Π»Π½ΠΈΡ
Π΄ΠΎΠΏΡΠΈΠ½ΠΎΡΠ° ΡΠ΅Π·Π΅ ΠΊΠΎΡΠΈ ΡΡ ΠΌΠΎΡΠΈΠ²ΠΈΡΠ°Π½ΠΈ ΡΠΈΡΠ΅Π½ΠΈΡΠΎΠΌ Π΄Π° Π°Π½Π°Π»ΠΈΠ·Π° ΠΎΠ±Π»ΠΈΠΊΠ° ΡΡΠ°Π΄ΠΈΡΠΈΠΎΠ½Π°Π»Π½ΠΎ ΠΏΡΠ΅ΡΠΏΠΎΡΡΠ°Π²ΡΠ° Π΄Π° ΡΡ ΠΎΠ±ΡΠ΅ΠΊΡΠΈ Π½Π° ΡΠ»ΠΈΡΠΈ ΠΏΡΠ΅ΡΡ
ΠΎΠ΄Π½ΠΎ ΡΠ΅Π΄Π½ΠΎΠ·Π½Π°ΡΠ½ΠΎ ΠΈ ΡΠ°ΡΠ½ΠΎ ΠΈΠ·Π΄Π²ΠΎΡΠ΅Π½ΠΈ ΠΈΠ· ΡΠ»ΠΈΠΊΠ΅. Π’Π°ΠΊΠ²ΠΎ ΠΈΠ·Π΄Π²Π°ΡΠ°ΡΠ΅ ΠΎΠ±ΡΠ΅ΠΊΠ°ΡΠ° ΡΠ΅ ΠΎΠ±ΠΈΡΠ½ΠΎ ΠΏΠΎΡΡΠΈΠΆΠ΅ Ρ ΠΏΡΠΎΡΠ΅ΡΡ ΡΠ°ΡΠ½Π΅ (ΡΠΎ ΡΠ΅ΡΡ Π±ΠΈΠ½Π°ΡΠ½Π΅) ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ°ΡΠΈΡΠ΅ ΠΎΡΠΈΠ³ΠΈΠ½Π°Π»Π½Π΅ ΡΠ»ΠΈΠΊΠ΅ Π³Π΄Π΅ ΡΠ΅ ΠΎΠ΄Π»ΡΠΊΠ° ΠΎ ΠΏΡΠΈΠΏΠ°Π΄Π½ΠΎΡΡΠΈ ΡΠ°ΡΠΊΠ΅ ΠΎΠ±ΡΠ΅ΠΊΡΡ Π½Π° ΡΠ»ΠΈΡΠΈ Π΄ΠΎΠ½ΠΎΡΠΈ Π½Π° ΡΠ΅Π΄Π½ΠΎΠ·Π½Π°ΡΠ°Π½ ΠΈ Π½Π΅Π΄Π²ΠΎΡΠΌΠΈΡΠ»Π΅Π½ΠΈ Π½Π°ΡΠΈΠ½. ΠΠ΅ΡΡΡΠΈΠΌ, ΡΡΠ»Π΅Π΄ Π½Π΅ΡΠ°Π²ΡΡΠ΅Π½ΠΎΡΡΠΈ ΡΡΠ»ΠΎΠ²Π° ΠΈΠ»ΠΈ ΡΡΠ΅ΡΠ°ΡΠ° Π·Π° ΡΠ½ΠΈΠΌΠ°ΡΠ΅, ΠΏΡΠΈΡΡΡΡΠ²Π° ΡΡΠΌΠ° ΠΈ ΡΠ°Π·Π»ΠΈΡΠΈΡΠΈΡ
Π²ΡΡΡΠ° Π½Π΅ΠΏΡΠ΅ΡΠΈΠ·Π½ΠΎΡΡΠΈ (Π½Π° ΠΏΡΠΈΠΌΠ΅Ρ Π½Π΅ΠΏΠΎΡΡΠΎΡΠ°ΡΠ΅ ΠΏΡΠ΅ΡΠΈΠ·Π½Π΅ Π³ΡΠ°Π½ΠΈΡΠ΅ ΠΎΠ±ΡΠ΅ΠΊΡΠ° ΠΈΠ»ΠΈ ΡΠ°ΡΠ½ΠΈΡ
Π³ΡΠ°Π½ΠΈΡΠ° ΠΈΠ·ΠΌΠ΅ΡΡ ΡΠ°ΠΌΠΈΡ
ΠΎΠ±ΡΠ΅ΠΊΠ°ΡΠ°, Π³ΡΠ΅ΡΠΊΠ΅ Ρ ΡΠ°ΡΡΠ½Π°ΡΡ, Π½Π΅Π΄ΠΎΡΡΠ°ΡΠΊΠ° ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΡΠ°, ΠΈΡΠ΄.), ΠΌΠΎΠ³Ρ ΡΠ΅ ΠΏΠΎΡΠ°Π²ΠΈΡΠΈ ΡΠ°Π·Π»ΠΈΡΠΈΡΠΈ Π½ΠΈΠ²ΠΎΠΈ Π½Π΅ΡΠΈΠ³ΡΡΠ½ΠΎΡΡΠΈ ΠΈ Π½Π΅ΠΎΠ΄ΡΠ΅ΡΠ΅Π½ΠΎΡΡΠΈ Ρ ΠΏΡΠΎΡΠ΅ΡΡ Π΄ΠΎΠ½ΠΎΡΠ΅ΡΠ° ΠΎΠ΄Π»ΡΠΊΠ΅ Ρ Π²Π΅Π·ΠΈ ΡΠ° ΠΏΡΠΈΠΏΠ°Π΄Π½ΠΎΡΡΡ ΡΠ°ΡΠΊΠ΅ ΡΠ»ΠΈΠΊΠ΅. ΠΠ²ΠΎ ΡΠ΅ ΠΏΠΎΡΠ΅Π±Π½ΠΎ Π²ΠΈΠ΄ΡΠΈΠ²ΠΎ Ρ ΡΠ»ΡΡΠ°ΡΡ Π΄ΠΈΡΠΊΡΠ΅ΡΠΈΠ·Π°ΡΠΈΡΠ΅ (ΡΠΎ ΡΠ΅ΡΡ ΡΠ·ΠΎΡΠΊΠΎΠ²Π°ΡΠ°) Π½Π΅ΠΏΡΠ΅ΠΊΠΈΠ΄Π½ΠΎΠ³ Π΄ΠΎΠΌΠ΅Π½Π° ΡΠ»ΠΈΠΊΠ΅ ΠΊΠ°Π΄Π° Π΅Π»Π΅ΠΌΠ΅Π½Ρ ΡΠ»ΠΈΠΊΠ΅, ΠΏΡΠΈΠ΄ΡΡΠΆΠ΅Π½ ΠΎΠ΄Π³ΠΎΠ²Π°ΡΠ°ΡΡΡΠΎΡ ΡΠ°ΡΠΊΠΈ ΡΠ·ΠΎΡΠΊΠ° Π΄ΠΎΠΌΠ΅Π½Π°, ΠΌΠΎΠΆΠ΅ Π±ΠΈΡΠΈ Π΄Π΅Π»ΠΈΠΌΠΈΡΠ½ΠΎ ΠΏΠΎΠΊΡΠΈΠ²Π΅Π½ ΡΠ° Π²ΠΈΡΠ΅ ΠΎΠ±ΡΠ΅ΠΊΠ°ΡΠ° Π½Π° ΡΠ»ΠΈΡΠΈ. Π£ ΡΠΎΠΌ ΡΠΌΠΈΡΠ»Ρ, ΠΈΠΌΠ°ΠΌΠΎ Π΄Π° ΠΎΠ²Π° Π²ΡΡΡΠ° ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ°ΡΠΈΡΠ΅ ΠΌΠΎΠΆΠ΅ ΠΏΠΎΡΠ΅Π½ΡΠΈΡΠ°Π»Π½ΠΎ Π΄ΠΎΠ²Π΅ΡΡΠΈ Π΄ΠΎ ΠΏΠΎΠ³ΡΠ΅ΡΠ½Π΅ ΠΎΠ΄Π»ΡΠΊΠ΅ ΠΎ ΠΏΡΠΈΠΏΠ°Π΄Π½ΠΎΡΡΠΈ ΡΠ°ΡΠ°ΠΊΠ° ΡΠ»ΠΈΠΊΠ΅, Π° ΡΠ°ΠΌΠΈΠΌ ΡΠΈΠΌ ΠΈ Π½Π΅ΠΏΠΎΠ²ΡΠ°ΡΠ½ΠΎΠ³ Π³ΡΠ±ΠΈΡΠΊΠ° ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΡΠ° ΠΎ ΠΎΠ±ΡΠ΅ΠΊΡΠΈΠΌΠ° ΠΊΠΎΡΠΈ ΡΠ΅ Π½Π° ΡΠ»ΠΈΡΠΈ Π½Π°Π»Π°Π·Π΅. Π’ΠΎ ΠΏΡΠΎΠΈΠ·Π»Π°Π·ΠΈ ΠΈΠ· ΡΠΈΡΠ΅Π½ΠΈΡΠ΅ Π΄Π° ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ°ΡΠΈΡΠ° ΡΠ»ΠΈΠΊΠ΅ ΠΈΠ·Π²Π΅Π΄Π΅Π½Π° Π½Π° ΠΎΠ²Π°Ρ Π½Π°ΡΠΈΠ½ Π½Π΅ Π΄ΠΎΠ·Π²ΠΎΡΠ°Π²Π° Π΄Π° ΡΠ°ΡΠΊΠ° ΡΠ»ΠΈΠΊΠ΅ ΠΌΠΎΠΆΠ΅ Π΄Π΅Π»ΠΈΠΌΠΈΡΠ½ΠΎ Ρ ΠΎΠ΄ΡΠ΅ΡΠ΅Π½ΠΎΠΌ ΠΎΠ±ΠΈΠΌΡ Π±ΠΈΡΠΈ ΡΠ»Π°Π½ ΠΏΠΎΡΠΌΠ°ΡΡΠ°Π½ΠΎΠ³ ΠΎΠ±ΡΠ΅ΠΊΡΠ° Π½Π° ΡΠ»ΠΈΡΠΈ, ΡΡΠΎ Π΄Π°ΡΠ΅ Π²ΠΎΠ΄ΠΈ ΠΏΠΎΡΠ΅Π½ΡΠΈΡΠ°Π»Π½ΠΎΠΌ ΡΠΈΠ·ΠΈΠΊΡ Π΄Π° ΡΠ°ΡΠΊΠ΅ Π΄Π΅Π»ΠΈΠΌΠΈΡΠ½ΠΎ ΡΠ°Π΄ΡΠΆΠ°Π½Π΅ Ρ ΠΎΠ±ΡΠ΅ΠΊΡΡ ΠΏΡΠ΅ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ°ΡΠΈΡΠ΅ Π½Π΅ΡΠ΅ Π±ΠΈΡΠΈ ΠΏΡΠΈΠ΄ΡΡΠΆΠ΅Π½Π΅ ΠΎΠ±ΡΠ΅ΠΊΡΡ Π½Π°ΠΊΠΎΠ½ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ°ΡΠΈΡΠ΅. ΠΠ΅ΡΡΡΠΈΠΌ, Π°ΠΊΠΎ ΡΠ΅ ΡΠΌΠ΅ΡΡΠΎ Π±ΠΈΠ½Π°ΡΠ½Π΅ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ°ΡΠΈΡΠ΅ ΠΈΠ·Π²ΡΡΠΈ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ°ΡΠΈΡΠ° ΡΠ»ΠΈΠΊΠ΅ Π³Π΄Π΅ ΡΠ΅ ΠΎΠ΄Π»ΡΠΊΠ° ΠΎ ΠΏΡΠΈΠΏΠ°Π΄Π½ΠΎΡΡΠΈ ΡΠ°ΡΠΊΠ΅ ΡΠ»ΠΈΠΊΠ΅ ΠΎΠ±ΡΠ΅ΠΊΡΡ Π΄ΠΎΠ½ΠΎΡΠΈ Π½Π° Π½Π°ΡΠΈΠ½ ΠΊΠΎΡΠΈ ΠΎΠΌΠΎΠ³ΡΡΠ°Π²Π° Π΄Π° ΡΠ°ΡΠΊΠ° ΠΌΠΎΠΆΠ΅ Π΄Π΅Π»ΠΈΠΌΠΈΡΠ½ΠΎ Π±ΠΈΡΠΈ ΡΠ»Π°Π½ ΠΎΠ±ΡΠ΅ΠΊΡΠ° Ρ Π½Π΅ΠΊΠΎΠΌ ΠΎΠ±ΠΈΠΌΡ, ΡΠ°Π΄Π° ΡΠ΅ Π΄ΠΎΠ½ΠΎΡΠ΅ΡΠ΅ Π±ΠΈΠ½Π°ΡΠ½Π΅ ΠΎΠ΄Π»ΡΠΊΠ΅ ΠΎ ΡΠ»Π°Π½ΡΡΠ²ΠΎ ΡΠ°ΡΠΊΠ΅ ΠΎΠ±ΡΠ΅ΠΊΡΡ Π½Π° ΡΠ»ΠΈΡΠΈ ΠΌΠΎΠΆΠ΅ ΠΈΠ·Π±Π΅ΡΠΈ Ρ ΠΎΠ²ΠΎΠΌ ΡΠ°Π½ΠΎΠΌ ΠΊΠΎΡΠ°ΠΊΡ Π°Π½Π°Π»ΠΈΠ·Π΅. Π’ΠΎ Π΄Π°ΡΠ΅ ΡΠ΅Π·ΡΠ»ΡΠΈΡΠ° Π΄Π° ΡΠ΅ ΠΏΠΎΡΠ΅Π½ΡΠΈΡΠ°Π»Π½ΠΎ Π²Π΅Π»ΠΈΠΊΠ° ΠΊΠΎΠ»ΠΈΡΠΈΠ½Π° ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΡΠ° ΠΎ ΠΎΠ±ΡΠ΅ΠΊΡΠΈΠΌΠ° ΠΏΡΠΈΡΡΡΠ½ΠΈΠΌ Π½Π° ΡΠ»ΠΈΡΠΈ ΠΌΠΎΠΆΠ΅ ΡΠ°ΡΡΠ²Π°ΡΠΈ Π½Π°ΠΊΠΎΠ½ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ°ΡΠΈΡΠ΅, ΠΈ ΠΊΠΎΡΠΈΡΡΠΈΡΠΈ Ρ ΡΠ»Π΅Π΄Π΅ΡΠΈΠΌ ΠΊΠΎΡΠ°ΡΠΈΠΌΠ° Π°Π½Π°Π»ΠΈΠ·Π΅. Π‘ ΡΠΈΠΌ Ρ Π²Π΅Π·ΠΈ, ΠΎΠ΄ ΠΏΠΎΡΠ΅Π±Π½ΠΎΠ³ ΠΈΠ½ΡΠ΅ΡΠ΅ΡΠ° Π·Π° Π½Π°Ρ ΡΠ΅ΡΡΠ΅ ΡΠΏΠ΅ΡΠΈΡΠ°Π»Π½Π° Π²ΡΡΡΠ° ΡΠ°Π·ΠΈ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ°ΡΠΈΡΠ΅ ΡΠ»ΠΈΠΊΠ΅, ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ°ΡΠΈΡΠ° Π·Π°ΡΠ½ΠΎΠ²Π°Π½Π° Π½Π° ΠΏΠΎΠΊΡΠΈΠ²Π΅Π½ΠΎΡΡΠΈ Π΅Π»Π΅ΠΌΠ΅Π½Π°ΡΠ° ΡΠ»ΠΈΠΊΠ΅, ΠΊΠΎΡΠ° ΠΊΠ°ΠΎ ΡΠ΅Π·ΡΠ»ΡΠ°Ρ ΠΎΠ±Π΅Π·Π±Π΅ΡΡΡΠ΅ ΡΠ°Π·ΠΈ Π΄ΠΈΠ³ΠΈΡΠ°Π»Π½Ρ ΡΠ΅ΠΏΡΠ΅Π·Π΅Π½ΡΠ°ΡΠΈΡΡ ΡΠ»ΠΈΠΊΠ΅ Π³Π΄Π΅ ΡΠ΅ Π²ΡΠ΅Π΄Π½ΠΎΡΡ ΡΠ»Π°Π½ΡΡΠ²Π° Π΄ΠΎΠ΄Π΅ΡΠ΅Π½Π° ΡΠ²Π°ΠΊΠΎΠΌ Π΅Π»Π΅ΠΌΠ΅Π½ΡΡ ΠΏΡΠΎΠΏΠΎΡΡΠΈΠΎΠ½Π°Π»Π½Π° ΡΠ΅Π³ΠΎΠ²ΠΎΡ ΡΠ΅Π»Π°ΡΠΈΠ²Π½ΠΎΡ ΠΏΠΎΠΊΡΠΈΠ²Π΅Π½ΠΎΡΡΠΈ Π½Π΅ΠΏΡΠ΅ΠΊΠΈΠ΄Π½ΠΈΠΌ ΠΎΠ±ΡΠ΅ΠΊΡΠΎΠΌ Π½Π° ΠΎΡΠΈΠ³ΠΈΠ½Π°Π»Π½ΠΎΡ ΡΠ»ΠΈΡΠΈ. Π£ ΠΎΠ²ΠΎΡ ΡΠ΅Π·ΠΈ Π±Π°Π²ΠΈΠΌΠΎ ΡΠ΅ ΠΈΡΡΡΠ°ΠΆΠΈΠ²Π°ΡΠ΅ΠΌ ΠΌΠΎΠ΄Π΅Π»Π° Π΄ΠΈΠ³ΠΈΡΠ°Π»ΠΈΠ·Π°ΡΠΈΡΠ΅ ΠΏΠΎΠΊΡΠΈΠ²Π΅Π½ΠΎΡΡΠΈ ΠΊΠΎΡΠΈ ΠΏΡΡΠΆΠ° ΠΎΠ²Π°ΠΊΠ²Ρ Π²ΡΡΡΡ ΡΠ΅ΠΏΡΠ΅Π·Π΅Π½ΡΠ°ΡΠΈΡΡ ΡΠ»ΠΈΠΊΠ΅ ΠΈ ΠΏΡΠ΅Π΄ΡΡΠ°Π²ΡΠ°ΠΌΠΎ ΠΊΠ°ΠΊΠΎ ΡΠ΅ ΠΌΠΎΠ³Ρ ΠΏΠΎΡΡΠΈΡΠΈ Π·Π½Π°ΡΠ°ΡΠ½Π° ΠΏΠΎΠ±ΠΎΡΡΠ°ΡΠ° Ρ ΠΎΡΠ΅Π½ΠΈ 3Π ΠΠΠ’, ΠΊΠ°ΠΎ ΠΈ ΡΠΈΠ³Π½Π°ΡΡΡΠ΅ Π½Π΅ΠΏΡΠ΅ΠΊΠΈΠ΄Π½ΠΎΠ³ ΠΎΠ±Π»ΠΈΠΊΠ° Π·Π°ΡΠ½ΠΎΠ²Π°Π½Π΅ Π½Π° ΡΠ°ΡΡΠΎΡΠ°ΡΡ ΠΎΠ΄ ΡΠ΅Π½ΡΡΠΎΠΈΠ΄Π°, Π°ΠΊΠΎ ΡΡ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΡΠ΅ ΠΎ ΠΏΠΎΠΊΡΠΈΠ²Π΅Π½ΠΎΡΡΠΈ Π΄ΠΎΡΡΡΠΏΠ½Π΅ Ρ ΠΎΠ²ΠΎΡ ΡΠ΅ΠΏΡΠ΅Π·Π΅Π½ΡΠ°ΡΠΈΡΠΈ ΡΠ»ΠΈΠΊΠ΅ ΡΠ°Π·ΠΌΠ°ΡΡΠ°Π½Π΅ Π½Π° ΠΎΠ΄Π³ΠΎΠ²Π°ΡΠ°ΡΡΡΠΈ Π½Π°ΡΠΈΠ½.Doktorska disertacija se bavi prouΔavanjem kvantitativnih aspekata atributa oblika pogodnih za numeriΔku karakterizaciju, to jest deskriptora oblika, kao i teorijom neodreΔenosti, posebno teorijom fazi skupova, i njihovom primenom u obradi slike. Originalni doprinosi i rezultati teze mogu se prirodno podeliti u dve grupe, u skladu sa pristupom i metodologijom koja je koriΕ‘Δena za njihovo dobijanje. Prva grupa doprinosa odnosi se na uvoΔenje novih deskriptora oblika (Ε‘estougaonosti i fazi kvadratnosti) kao i odgovarajuΔih mera koje numeriΔki ocenjuju u kom obimu razmatrani oblik zadovoljava razmatrana svojstva. Uvedene mere su prirodno definisane, teorijski dobro zasnovane i zadovoljavaju veΔinu poΕΎeljnih svojstava koje svaka dobro definisana mera oblika treba da zadovoljava. Pomenimo neke od njih: obe mere uzimaju vrednosti iz intervala (0,1] i dostiΕΎu najveΔu moguΔu vrednost 1 ako i samo ako je oblik koji se posmatra Ε‘estougao, odnosno fazi kvadrat; ne postoji oblik ne-nula povrΕ‘ine Δija je izmerena Ε‘estougaonost, odnosno fazi kvadratnost jednaka 0; obe uvedene mere su invarijantne u odnosu na transformacije sliΔnosti; i daju rezultate koji su u skladu sa teorijski dokazanim rezultatima, kao i ljudskom percepcijom i oΔekivanjima. Brojni eksperimenti na sintetiΔkim i realnim primerima prikazani su u cilju ilustrovanja teorijski dokazanih razmatranja i pruΕΎanja jasnijeg uvida u ponaΕ‘anje uvedenih mera. NJihova prednost i korisnost ilustrovani su u razliΔitim zadacima prepoznavanja i klasifikacije slika objekata nekoliko poznatih i najΔeΕ‘Δe koriΕ‘Δenih baza slika. Pored toga, doktorska teza sadrΕΎi istraΕΎivanja vezana za primenu teorije neodreΔenosti, u uΕΎem smislu teorije fazi skupova, u razliΔitim zadacima obrade slike i analize oblika. Razlikujemo zadatke koji se odnose na izdvajanje karakteristika oblika i one koji se odnose na poboljΕ‘anje performansi razliΔitih tehnika obrade i analize slike. Ε to se tiΔe prve grupe zadataka, bavimo se primenom teorije fazi skupova u zadacima definisanja novog deskriptora fazi oblika, nazvan fazi kvadratnost, i merenja koliko je fazi kvadratan posmatrani fazi oblik. U drugoj grupi zadataka bavimo se istraΕΎivanjem poboljΕ‘anja performansi ocene transformacije slike euklidskim rastojanjima u tri dimenzije (3D EDT), kao i signature neprekidnog oblika u dve dimenzije zasnovane na rastojanju od centroida oblika. Ovo poslednje se posebno ogleda u postignutoj taΔnosti i preciznosti ocene, poveΔanoj invarijantnosti u odnosu na rotaciju i translaciju objekta, kao i robustnosti u prisustvu Ε‘uma i neodreΔenosti koje su posledica nesavrΕ‘enosti ureΔaja ili uslova snimanja. Poslednji rezultati se takoΔe odnose i na drugu grupu originalnih doprinosa teze koji su motivisani Δinjenicom da analiza oblika tradicionalno pretpostavlja da su objekti na slici prethodno jednoznaΔno i jasno izdvojeni iz slike. Takvo izdvajanje objekata se obiΔno postiΕΎe u procesu jasne (to jest binarne) segmentacije originalne slike gde se odluka o pripadnosti taΔke objektu na slici donosi na jednoznaΔan i nedvosmisleni naΔin. MeΔutim, usled nesavrΕ‘enosti uslova ili ureΔaja za snimanje, prisustva Ε‘uma i razliΔitih vrsta nepreciznosti (na primer nepostojanje precizne granice objekta ili jasnih granica izmeΔu samih objekata, greΕ‘ke u raΔunanju, nedostatka informacija, itd.), mogu se pojaviti razliΔiti nivoi nesigurnosti i neodreΔenosti u procesu donoΕ‘enja odluke u vezi sa pripadnoΕ‘Δu taΔke slike. Ovo je posebno vidljivo u sluΔaju diskretizacije (to jest uzorkovanja) neprekidnog domena slike kada element slike, pridruΕΎen odgovarajuΔoj taΔki uzorka domena, moΕΎe biti delimiΔno pokriven sa viΕ‘e objekata na slici. U tom smislu, imamo da ova vrsta segmentacije moΕΎe potencijalno dovesti do pogreΕ‘ne odluke o pripadnosti taΔaka slike, a samim tim i nepovratnog gubitka informacija o objektima koji se na slici nalaze. To proizlazi iz Δinjenice da segmentacija slike izvedena na ovaj naΔin ne dozvoljava da taΔka slike moΕΎe delimiΔno u odreΔenom obimu biti Δlan posmatranog objekta na slici, Ε‘to dalje vodi potencijalnom riziku da taΔke delimiΔno sadrΕΎane u objektu pre segmentacije neΔe biti pridruΕΎene objektu nakon segmentacije. MeΔutim, ako se umesto binarne segmentacije izvrΕ‘i segmentacija slike gde se odluka o pripadnosti taΔke slike objektu donosi na naΔin koji omoguΔava da taΔka moΕΎe delimiΔno biti Δlan objekta u nekom obimu, tada se donoΕ‘enje binarne odluke o Δlanstvo taΔke objektu na slici moΕΎe izbeΔi u ovom ranom koraku analize. To dalje rezultira da se potencijalno velika koliΔina informacija o objektima prisutnim na slici moΕΎe saΔuvati nakon segmentacije, i koristiti u sledeΔim koracima analize. S tim u vezi, od posebnog interesa za nas jeste specijalna vrsta fazi segmentacije slike, segmentacija zasnovana na pokrivenosti elemenata slike, koja kao rezultat obezbeΔuje fazi digitalnu reprezentaciju slike gde je vrednost Δlanstva dodeljena svakom elementu proporcionalna njegovoj relativnoj pokrivenosti neprekidnim objektom na originalnoj slici. U ovoj tezi bavimo se istraΕΎivanjem modela digitalizacije pokrivenosti koji pruΕΎa ovakvu vrstu reprezentaciju slike i predstavljamo kako se mogu postiΔi znaΔajna poboljΕ‘anja u oceni 3D EDT, kao i signature neprekidnog oblika zasnovane na rastojanju od centroida, ako su informacije o pokrivenosti dostupne u ovoj reprezentaciji slike razmatrane na odgovarajuΔi naΔin
On Discrete Moments of Unbounded Order
Abstract. Moment-based procedures are commonly used in computer vision, image analysis, or pattern recognition. Basic shape features such as size, position, orientation, or elongation are estimated by moments of order β€ 2. Shape invariants are defined by higher order moments. In contrast to a theory of moments in continuous mathematics, shape moments in imaging have to be estimated from digitized data. Infinitely many different shapes in Euclidean space are represented by an identical digital shape. There is an inherent loss of information, impacting moment estimation. This paper discusses accuracy limitations in moment reconstruction in dependency of order of reconstructed moments and applied resolution of digital pictures. We consider moments of arbitrary order, which is not assumed to be bounded by a constant