Solutions to some problems on unique representation bases

Wavelet packets provide a flexible representation of data, which has been proved to be very useful in a lot of applications in signal, image and video processing. In particular, in image and video coding, their ability to best capture the input content features can be exploited by designing appropriate optimization criteria. In this paper, we introduce joint wavelet packets for groups of frames, allowing to provide a unique best basis representation for several frames and not one basis per frame, as classically done. Two main advantages are expected from this joint representation. On the one hand, bitrate is spared, since a single tree description is sent instead of 31 per group of frames (GOP) - when a GOP contains, for example, 32 frames. On the other hand, this common description can characterize the spatio-temporal features of the given video GOP and this way can be exploited as a valuable feature for video classification and video database searching. A second contribution of the paper is to provide insight into the modifications necessary in the best basis algorithm (BBA) in order to cope with biorthogonal decompositions. A computationally efficient algorithm is deduced for an entropy-based criterion.

Arbitrarily sparse sets A of integers are constructed with the property that every integer can be represented uniquely in the form n = a + a', where a and a' belong to the set A and a < a' or a = a'. Some related open problems are stated.

Objectives The present study established an interpretation system for the Human Figure Drawing test, developed a scoring guide, and validated its effectiveness. Methods This study selected basic and unique representations expressed in the Human Figure Drawing test based on literature review and previous research. Through expert evaluation, a scoring guide for the interpretation system of the Human Figure Drawing test was developed, consisting of 53 items representing 9 key indicators of emotional and personality aspects (aggression, anxiety, depression, interpersonal avoidance, diminished self-esteem, emotional instability, affection deficiency, inferiority, regression). To validate this system, the study included 343 participants (173 boys and 170 girls) from 4th, 5th, and 6th grades in elementary schools located in Seoul. Results The results of the study are as follows. First, the results of the self-report questionnaire test followed a normal distribution. Second, the analysis of the scoring results from the self-report questionnaire test and the Human Figure Drawing test showed significant correlations. Aggression was significantly correlated with the representations of aggression, anxiety, and depression in the Human Figure Drawing test. Interpersonal relationships were significantly correlated with the representations of anxiety and depression. Social anxiety was significantly correlated with the representations of aggression, anxiety, depression, interpersonal avoidance, diminished self-esteem, emotional instability, inferiority, and regression. Additionally, self-esteem showed a significant negative correlation with the representations of anxiety, depression, interpersonal avoidance, diminished self-esteem, emotional instability, affection deficiency, inferiority, and regression in the Human Figure Drawing test. Depression was significantly correlated with the representations of anxiety, depression, interpersonal avoidance, diminished self-esteem, emotional instability, affection deficiency, and inferiority. It was observed that social anxiety, self-esteem, and depression could be more clearly diagnosed through the scoring guide of the interpretation system of the Human Figure Drawing test. Conclusions Despite various research results on the Human Figure Drawing test, there has been no process to concretely score and generalize its findings. This study validated that process, demonstrating that the Human Figure Drawing test can diagnose levels of aggression, interpersonal relationships, social anxiety, self-esteem, and depression in participants. It is highly significant that an interpretation system was created that allows for diagnosis based on the scoring guide, even without expert input. However, it should be noted that this study was limited to upper elementary school students.