A new family of distance functions for perceptual similarity retrieval of medical images

Abstract

A long-standing challenge of content-based image retrieval (CBIR) systems is the definition of a suitable distance function to measure the similarity between images in an application context which complies with the human perception of similarity. In this paper, we present a new family of distance functions, called attribute concurrence influence distances (AID), which serve to retrieve images by similarity. These distances address an important aspect of the psychophysical notion of similarity in comparisons of images: the effect of concurrent variations in the values of different image attributes. The AID functions allow for comparisons of feature vectors by choosing one of two parameterized expressions: one targeting weak attribute concurrence influence and the other for strong concurrence influence. This paper presents the mathematical definition and implementation of the AID family for a two-dimensional feature space and its extension to any dimension. The composition of the AID family with L (p) distance family is considered to propose a procedure to determine the best distance for a specific application. Experimental results involving several sets of medical images demonstrate that, taking as reference the perception of the specialist in the field (radiologist), the AID functions perform better than the general distance functions commonly used in CBIR.

Fig 1

Example of a CBIR environment.

Fig 2

Geometric equidistant places defined by different values of p, considering a two-dimensional space (only the first quadrant is shown).

Fig 3

Degrees of AC.

Fig 4

WAID and SAID curves. Only the first octant (|q_x − c_x| > |q_y − c_y|) is represented. In the other octants, the identity lines mirror the curves.

Fig 5

Degree of ACI—geometric place of points located at distance d for different values of n: a SAID family, b WAID family.

Fig 6

Conditions to determine the general expression of SAID family.

Fig 7

Conditions to determine the general expression of WAID family.

Fig 8

Comparison of L₁, L₂, and .

Fig 9

Composition of L_p and AID.

Fig 10

Variations of distance between C and Q using the distance functions of L_p and AID families represented in the first octant of 2-D space.

Fig 11

Samples of images from the set of tests with texture attributes.

Fig 12

Curves of precision in evaluating the accuracy of distances. Each curve corresponds to the results of one radiologist (R1 to R5).

Fig 13

Precision in determining the best function regarding parameter n (the five radiologists were considered).

Fig 14

Precision of four texture attributes.

Fig 15

Precision vs recall for image segmentation.

Fig 16

Samples of lung ROIs presenting specific pathologies.

Fig 17

Precision vs recall for wavelets and histogram gradient descriptors.