You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


1. Field of the Invention
The present invention relates to an image coding apparatus utilizing global motion vector upon coding of image inputted by means of motion vector.
2. Description of the Related Art
Conventionally, in high-efficiency coding of image, the following three image transformations are mainly used for compressing amounts of moving image information, thereby carrying out coding. Therefore, the three image transformations are the first image transformation by means of correlation of image (spatial correlation), the second image transformation by means of correlation between times (time correlation), and the third image transformation by means of variable length coding. Specifically, in the second coding by means of time correlation, moving direction and moving distance of image between temporally-different frames (inputted images) are detected as ‘motion vector’ on a macro block basis, and a frame is expressed based on pixel information of the macro block and the motion vector information, thereby reducing the amount of image information.
However, in the detection process of the ‘motion vector’, when detecting a block in the other frame, a destination (or a source) of the macro block, for example, in the case of moving image including dynamic scenes such as a sports moving image, it is required to set a wide search range, thereby greatly increasing amounts of the calculation. Therefore, in WO00/05899, it is disclosed that the global motion vector of the entire image is detected by means of the reduced image of the current frame, and the search range of destination of the macro block is narrowed by means of the global motion vector, thereby detecting the motion vector.
FIG. 17 is a diagram exemplifying another detection of motion vector of the macro block by means of the above global motion vector. As shown FIG. 17 (a), at the outset, the global motion vector (1701) of the global macro block α′ including the macro block α, of which motion vector is to be detected, is detected. Therefore, it is probable that the macro block α moves within a predetermined range including the destination of the global macro block α′ indicated by this global motion vector. Therefore, calculation of the range β of FIG. 17 (b) as the search range of the motion vector of the macro block α is carried out, so that it becomes possible to detect the motion vector (1702) of the macro block α without unnecessarily widening search range.
However, in the above detection of the global motion vector used for the second image transformation, the detector for the global motion vector is arranged in the same chip of the image transformer utilizing spatial correlation as the first image transformation technology, resulting in two problems: they are as follows. The first problem is that a frame referenced upon detection of the global motion vector is not perfectly identical to an inputted image. The reason for this is that the referenced frame is reproduced by inverse transformation of data coded by irreversible transformation by means of the spatial correlation, in which high-frequency components acquired by DCT (Discrete Cosine Transform) are removed, and the remainder is cut by quantization, so that the frame is possibly not the same image as the source frame. Therefore, error can be observed in the global motion vector, which is detected by referring to the reference frame, incorrectly reproduced as described above.
In addition, the second problem is that the detection of the global motion vector is carried out upon high-efficiency coding of image even if the detection of the global motion vector is unnecessary. For example, in the case of a moving image configured by high-vision images of 1,920×1,080 pixels, the maximum moving distance on a pixel basis is 1,920 in a horizontal direction, and 1,080 in a vertical direction (therefore, on a ½-pixel basis, the moving distance is double), so that it is required to set wide search range. Meanwhile, in the case of a moving image configured by images of 320×240 pixels, the maximum moving distance on a pixel basis is 320 in a horizontal direction, and 240 in a vertical direction, so that it is enough to set narrow search range for detecting the moving distance of an image on a pixel basis (or on a ½-pixel basis, or on a ¼-pixel basis) in comparison with the above case, even if the movement of the image is same as the above case. Alternatively, there is a significant difference between the average moving distance in a moving image of a news program shot in a studio and that of a sports program. Thus, depending on type of moving image, the search range can be different. Accordingly, there is a case where it is enough to carry out detection of motion vector on a normal macro block basis without carrying out detection of global motion vector, thereby reducing the calculation amount.